Relevant bibliographies by topics / Polynomials in Banach spaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Polynomials in Banach spaces'

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Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Polynomials in Banach spaces"

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Gonz´lez, Manuel, and Joaquín M. Gutiérrez. "Unconditionally converging polynomials on Banach spaces." Mathematical Proceedings of the Cambridge Philosophical Society 117, no. 2 (March 1995): 321–31. http://dx.doi.org/10.1017/s030500410007314x.

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In the study of polynomials acting on Banach spaces, the weak topology is not such a good tool as in the case of linear operators, due to the bad behaviour of the polynomials with respect to the weak convergence. For example,is a continuous polynomial taking a weakly null sequence into a sequence having no weakly Cauchy subsequences. In this paper we show that the situation is not so bad for unconditional series. Recall that is a weakly unconditionally Cauchy series (in short a w.u.C. series) in a Banach space E if for every f ε E* we have that and is an unconditionally converging series (in short an u.c. series) if every subseries is norm convergent.
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Kravtsiv, V. "Zeros of block-symmetric polynomials on Banach spaces." Matematychni Studii 53, no. 2 (June 24, 2020): 206–11. http://dx.doi.org/10.30970/ms.53.2.206-211.

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We investigate sets of zeros of block-symmetric polynomials on the direct sums of sequence spaces. Block-symmetric polynomials are more general objects than classical symmetric polynomials.An analogues of the Hilbert Nullstellensatz Theorem for block-symmetric polynomials on $\ell_p(\mathbb{C}^n)=\ell_p \oplus \ldots \oplus \ell_p$ and $\ell_1 \oplus \ell_{\infty}$ is proved. Also, we show that if a polynomial $P$ has a block-symmetric zero set then it must be block-symmetric.
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Peris, Alfredo. "Chaotic polynomials on Banach spaces." Journal of Mathematical Analysis and Applications 287, no. 2 (November 2003): 487–93. http://dx.doi.org/10.1016/s0022-247x(03)00547-x.

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Carando, Daniel. "Extendible Polynomials on Banach Spaces." Journal of Mathematical Analysis and Applications 233, no. 1 (May 1999): 359–72. http://dx.doi.org/10.1006/jmaa.1999.6319.

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FABIAN, M., D. PREISS, J. H. M. WHTTFIELD, and V. E. ZIZLER. "SEPARATING POLYNOMIALS ON BANACH SPACES." Quarterly Journal of Mathematics 40, no. 4 (1989): 409–22. http://dx.doi.org/10.1093/qmath/40.4.409.

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González, Manuel, and Joaquín M. Gutiérrez. "Orlicz-Pettis Polynomials on Banach Spaces." Monatshefte f�r Mathematik 129, no. 4 (May 9, 2000): 341–50. http://dx.doi.org/10.1007/s006050050080.

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Bu, Qingying, Gerard Buskes, and Yongjin Li. "Abstract M- and Abstract L-Spaces of Polynomials on Banach Lattices." Proceedings of the Edinburgh Mathematical Society 58, no. 3 (February 13, 2015): 617–29. http://dx.doi.org/10.1017/s0013091514000297.

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AbstractIn this paper we use the norm of bounded variation to study multilinear operators and polynomials on Banach lattices. As a result, we obtain when all continuous multilinear operators and polynomials on Banach lattices are regular. We also provide new abstract M- and abstract L-spaces of multilinear operators and polynomials and generalize all the results by Grecu and Ryan, from Banach lattices with an unconditional basis to all Banach lattices.
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Yadav, Sarjoo Prasad. "On the denseness of Jacobi polynomials." International Journal of Mathematics and Mathematical Sciences 2004, no. 28 (2004): 1455–62. http://dx.doi.org/10.1155/s0161171204305314.

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LetXrepresent either a spaceC[−1,1]orLα,βp(w),1≤p<∞, of functions on[−1,1]. It is well known thatXare Banach spaces under the sup and thep-norms, respectively. We prove that there exist the best possible normalized Banach subspacesXα,βkofXsuch that the system of Jacobi polynomials is densely spread on these, or, in other words, eachf∈Xα,βkcan be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Explicit representation forf∈Xα,βkhas been given.
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Sarantopoulos, Yannis. "Bounds on the derivatives of polynomials on Banach spaces." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 2 (September 1991): 307–12. http://dx.doi.org/10.1017/s0305004100070389.

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AbstractWe generalize the classical Bernstein's and Markov's Inequalities for polynomials on any real Banach space. We also give estimates for the derivatives of homogeneous polynomials on real Banach spaces.
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Boyd, C., and R. A. Ryan. "THE NORM OF THE PRODUCT OF POLYNOMIALS IN INFINITE DIMENSIONS." Proceedings of the Edinburgh Mathematical Society 49, no. 1 (February 2006): 17–28. http://dx.doi.org/10.1017/s0013091504000756.

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AbstractGiven a Banach space $E$ and positive integers $k$ and $l$ we investigate the smallest constant $C$ that satisfies $\|P\|\hskip1pt\|Q\|\le C\|PQ\|$ for all $k$-homogeneous polynomials $P$ and $l$-homogeneous polynomials $Q$ on $E$. Our estimates are obtained using multilinear maps, the principle of local reflexivity and ideas from the geometry of Banach spaces (type and uniform convexity). We also examine the analogous problem for general polynomials on Banach spaces.
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Dissertations / Theses on the topic "Polynomials in Banach spaces"

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Sarantopoulos, I. C. "Polynomials and multilinear mappings in Banach spaces." Thesis, Brunel University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376057.

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Berrios, Yana Sonia Sarita. "Funções holomorfas fracamente continuas em espaços de Banach." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307331.

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Orientador: Jorge Tulio Mujica Ascui
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Sejam E e F espaços de Banach complexos, e seja U um aberto em E. Neste trabalho estudamos os subespaços Hwu(U; F), Hw(U; F), Hwsc(U; F) e HwC(U; F) de H(U; F). Mais especificamente, se U é aberto equilibrado caracterizamos funções destes subespaços em termos de condições de equicontinuidade dos polinômios da série de Taylor. Estudamos sob que condições estes subespaços coincidem, estendendo assim os resultados dados em Aron, Herves e Valdivia [2] ao caso de abertos equilibrados. Se E tem uma base contrátil e incondicional, e U é uma bola aberta em E mostramos que cada função holomorfa f : U 'seta' F que é limitada nos conjuntos fracamente compactos U-limitados é limitada nos conjuntos U-limitados. Consequentemente, Hw(U; F) = Hwu(U; F)
Abstract: Let E and F be complex Banach spaces, and let U be an open set in E. In this work we study the subspaces Hwu(U; F), Hw(U; F), Hwsc(U; F) and HwC(U; F) of H(U; F). More specifically, if U is a balanced open set we characterize functions of these subespaces in terms of equicontinuity conditions of the polynomials in the Taylor series. We study under which conditions these subspaces coincide, and then we extend the results given in Aron, Herves and Valdivia [2] to the case of balanced open sets. If E has a shrinking and unconditional basis, and U is an open ball in E we show that each holomorphic function f : U 'seta' F that is bounded on weakly compact U-bounded sets is bounded on U-bounded sets. Consequently, Hw(U; F) = Hwu(U; F)
Doutorado
Doutor em Matemática
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Santos, Elisa Regina dos 1984. "A equação de Daugavet para polinômios em espaços de Banach." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307318.

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Orientador: Jorge Tulio Ascui Mujica
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Doutorado
Matematica
Doutor em Matemática
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Kaufmann, Pedro Levit. "Conjuntos de continuidade seqüencial fraca para polinômios em espaços de Banach." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-14032011-155222/.

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Esta dissertação tem por objetivo a apresentação de um estudo em espaços de Banach sobre os conjuntos nos quais determinados polinômios homogêneos contínuos são fracamente sequencialmente contínuos. Algumas propriedades desses conjuntos são estudadas e ilustradas com exemplos, em maior parte no espaço $l_p$. Obtemos um fórmula para o conjunto de continuidade sequencial fraca do produto de dois polinômios e algumas consequências. Resultados mais fortes são obtidos quando restringimos nossos espaços de Banach a espaços com FDD incondicional e/ou separáveis. Os resultados estudados aqui foram obtidos por R. Aron e V. Dimant em: Aron, R. & Dimant, V., Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299.
This work has the purpose of presenting a study on Banach spaces about sets in which determined homogeneous continuous polynomials are weakly sequentially continuous. Some properties of these sets are studied and illustrated with examples, most in the space $l_p$. We obtain a formula for the weak sequential continuity set of the product of two polynomials, and some consequences. Stronger results are obtained when we restrict our Banach spaces to spaces with unconditional FDD and/or separable. The results studied here were obtained by R. Aron and V. Dimant in: Aron, R. & Dimant, V., {Sets of weak sequential continuity for polynomials, Indag. Mathem., N.S., 13 (3) (2002), 287-299.
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Kuo, Po Ling. "Operadores de extensão de aplicações multilineares ou polinomios homogeneos." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307329.

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Orientador: Jorge Tulio Mujica Ascui
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho está dedicado ao estudo dos operadores de Nicodemi, introduzidos em [7] a partir de uma idéia em [12]. Os operadores de Nicodemi levam aplicações multilineares (resp. polinômios homogêneos) de um espaço de Banach E em aplicações multilineares (resp. polinômios homogêneos) em um espaço de Banach F. O nosso primeiro objetivo é encontrar condições para que os operadores de Nicodemi preservem certos tipos de aplicações multilineares (resp. polinômios homogêneos). Em particular estudamos a preservação de aplicações multilineares simétricas, de tipo finito, nucleares, compactas ou fracamente compactas. O segundo objetivo é encontrar condições para que, se os espaços duais E¿ e F¿ são isomorfos, os espaços de aplicações multilineares (resp. polinômios homogêneos) em E e F sejam isomorfos também. Estudamos também o problema correspondente para os espaços de aplicações multilineares (resp. polinômios homogêneos) de um determinado tipo, como por exemplo, de tipo finito, nuclear, compacto ou fracamente compacto
Abstract: This work is devoted to studying the Nicodemi operators, introduced in [7], following an idea in [12]. The Nicodemi operators map multilinear mappings (resp. homogeneous polynomials) on a Banach spaces E into multilinear mappings (resp. homogeneous polynomials) on a Banach spaces F. Our first objective is to find conditions under which the Nicodemi operators preserve certain types of multilinear mappings (resp. homogeneous polynomials). In particular we examine the preservation of the multilinear mappings that are symmetric, of finite type, nuclear, compact or weakly compact. Our second objective is tofind conditions under which, whenever the dual spaces E¿ and F¿ are isomorphic, the spaces of multilinear mappings (resp. homogeneous polynomials) on E and F are isomorphic as well. We also examine the corresponding problem for the spaces of multilinear mappings (resp. homogeneous polynomials) of a certain type, for instance of finite, nuclear, compact or weakly compact type
Doutorado
Analise Funcional
Doutor em Matemática
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Torres, Ewerton Ribeiro. "Hiper-ideais de aplicações multilineares e polinômios homogêneos em espaços de Banach." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05092016-143504/.

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Nesse trabalho introduzimos e desenvolvemos a teoria de hiper-ideais de aplicações multilineares contínuas e polinômios homogêneos contínuos entre espaços de Banach. A ideia central é refinar os conceitos de multi-ideais e de ideais de polinômios com o objetivo de explorar de forma mais aprofundada a natureza não-linear das aplicações envolvidas. Para isso tomamos a teoria de ideais de operadores lineares, aplicações multilineares e polinômios homogêneos, desenvolvida a partir dos trabalhos de Pietsch, tanto no caso linear como no caso multilinear, como referencial. Provamos resultados gerais para hiper-ideais, damos muitos exemplos ilustrativos, e desenvolvemos métodos para gerar hiper-ideais, tanto no caso multilinear como no caso polinomial.
In this work we introduce and develop the theory of hyper-ideals of multilinear mappings and homogeneous polynomials between Banach spaces. The main idea is to refine the concepts of multi-ideal and of ideal of polynomials with the purpose of exploring deeply the nonlinear nature of the underlying mappings. To do this we take the ideal theory of linear operators, multilinear mappings and homogeneous polynomials, developed from the works of Pietsch, both in the linear and nonlinear cases, as a reference. We prove general results for hyper-ideals, provide a number of illustrative examples, and develop methods to generate hyper-ideals of multilinear mappings, as well as of hyper-ideals of homogeneous polynomials.
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Zeekoei, Elroy Denovanne. "A study of Dunford-Pettis-like properties with applications to polynomials and analytic functions on normed spaces / Elroy Denovanne Zeekoei." Thesis, North-West University, 2011. http://hdl.handle.net/10394/7586.

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Recall that a Banach space X has the Dunford-Pettis property if every weakly compact operator defined on X takes weakly compact sets into norm compact sets. Some valuable characterisations of Banach spaces with the Dunford-Pettis property are: X has the DPP if and only if for all Banach spaces Y, every weakly compact operator from X to Y sends weakly convergent sequences onto norm convergent sequences (i.e. it requires that weakly compact operators on X are completely continuous) and this is equivalent to “if (xn) and (x*n) are sequences in X and X* respectively and limn xn = 0 weakly and limn x*n = 0 weakly then limn x*n xn = 0". A striking application of the Dunford-Pettis property (as was observed by Grothendieck) is to prove that if X is a linear subspace of L() for some finite measure  and X is closed in some Lp() for 1 ≤ p < , then X is finite dimensional. The fact that the well known spaces L1() and C() have this property (as was proved by Dunford and Pettis) was a remarkable achievement in the early history of Banach spaces and was motivated by the study of integral equations and the hope to develop an understanding of linear operators on Lp() for p ≥ 1. In fact, it played an important role in proving that for each weakly compact operator T : L1()  L1() or T : C()  C(), the operator T2 is compact, a fact which is important from the point of view that there is a nice spectral theory for compact operators and operators whose squares are compact. There is an extensive literature involving the Dunford-Pettis property. Almost all the articles and books in our list of references contain some information about this property, but there are plenty more that could have been listed. The reader is for instance referred to [4], [5], [7], [8], [10], [17] and [24] for information on the role of the DPP in different areas of Banach space theory. In this dissertation, however, we are motivated by the two papers [7] and [8] to study alternative Dunford-Pettis properties, to introduce a scale of (new) alternative Dunford-Pettis properties, which we call DP*-properties of order p (briefly denoted by DP*P), and to consider characterisations of Banach spaces with these properties as well as applications thereof to polynomials and holomorphic functions on Banach spaces. In the paper [8] the class Cp(X, Y) of p-convergent operators from a Banach space X to a Banach space Y is introduced. Replacing the requirement that weakly compact operators on X should be completely continuous in the case of the DPP for X (as is mentioned above) by “weakly compact operators on X should be p-convergent", an alternative Dunford-Pettis property (called the Dunford-Pettis property of order p) is introduced. More precisely, if 1 ≤ p ≤ , a Banach space X is said to have DPPp if the inclusion W(X, Y)  Cp(X, Y) holds for all Banach spaces Y . Here W(X, Y) denotes the family of all weakly compact operators from X to Y. We now have a scale of “Dunford-Pettis like properties" in the sense that all Banach spaces have the DPP1, if p < q, then each Banach space with the DPPq also has the DPPp and the strongest property, namely the DPP1 coincides with the DPP. In the paper [7] the authors study a property on Banach spaces (called the DP*-property, or briey the DP*P) which is stronger than the DPP, in the sense that if a Banach space has this property then it also has DPP. We say X has the DP*P, when all weakly compact sets in X are limited, i.e. each sequence (x*n)  X * in the dual space of X which converges weak* to 0, also converges uniformly (to 0) on all weakly compact sets in X. It turns out that this property is equivalent to another property on Banach spaces which is introduced in [17] (and which is called the *-Dunford-Pettis property) as follows: We say a Banach space X has the *-Dunford-Pettis property if for all weakly null sequences (xn) in X and all weak* null sequences (x*n) in X*, we have x*n(xn) n 0. After a thorough study of the DP*P, including characterisations and examples of Banach spaces with the DP*P, the authors in [7] consider some applications to polynomials and analytic functions on Banach spaces. Following an extensive literature study and in depth research into the techniques of proof relevant to this research field, we are able to present a thorough discussion of the results in [7] and [8] as well as some selected (relevant) results from other papers (for instance, [2] and [17]). This we do in Chapter 2 of the dissertation. The starting point (in Section 2.1 of Chapter 2) is the introduction of the so called p-convergent operators, being those bounded linear operators T : X  Y which transform weakly p-summable sequences into norm-null sequences, as well as the so called weakly p-convergent sequences in Banach spaces, being those sequences (xn) in a Banach space X for which there exists an x  X such that the sequence (xn - x) is weakly p-summable. Using these concepts, we state and prove an important characterisation (from the paper [8]) of Banach spaces with DPPp. In Section 2.2 (of Chapter 2) we continue to report on the results of the paper [7], where the DP*P on Banach spaces is introduced. We focus on the characterisation of Banach spaces with DP*P, obtaining among others that a Banach space X has DP*P if and only if for all weakly null sequences (xn) in X and all weak* null sequences (x*n) in X*, we have x*n(xn) n 0. An important characterisation of the DP*P considered in this section is the fact that X has DP*P if and only if every T  L(X, c0) is completely continuous. This result proves to be of fundamental importance in the study of the DP*P and its application to results on polynomials and holomorphic functions on Banach spaces. To be able to report on the applications of the DP*P in the context of homogeneous polynomials and analytic functions on Banach spaces, we embark on a study of “Complex Analysis in Banach spaces" (mostly with the focus on homogeneous polynomials and analytic functions on Banach spaces). This we do in Chapter 3; the content of the chapter is mostly based on work in the books [23] and [14], but also on the work in some articles such as [15]. After we have discussed the relevant theory of complex analysis in Banach spaces in Chapter 3, we devote Chapter 4 to considering properties of polynomials and analytic functions on Banach spaces with DP*P. The discussion in Chapter 4 is based on the applications of DP*P in the paper [7]. Finally, in Chapter 5 of the dissertation, we contribute to the study of “Dunford-Pettis like properties" by introducing the Banach space property “DP*P of order p", or briefly the DP*Pp for Banach spaces. Using the concept “weakly p-convergent sequence in Banach spaces" as is defined in [8], we define weakly-p-compact sets in Banach spaces. Then a Banach space X is said to have the DP*-property of order p (for 1 ≤ p ≤ ) if all weakly-p-compact sets in X are limited. In short, we say X has DP*Pp. As in [8] (where the DPPp is introduced), we now have a scale of DP*P-like properties, in the sense that all Banach spaces have DP*P1 and if p < q and X has DP*Pq then it has DP*Pp. The strongest property DP*P coincides with DP*P. We prove characterisations of Banach spaces with DP*Pp, discuss some examples and then consider applications to polynomials and analytic functions on Banach spaces. Our results and techniques in this chapter depend very much on the results obtained in the previous three chapters, but now we have to find our own correct definitions and formulations of results within this new context. We do this with some success in Sections 5.1 and 5.2 of Chapter 5. Chapter 1 of this dissertation provides a wide range of concepts and results in Banach spaces and the theory of vector sequence spaces (some of them very deep results from books listed in the bibliography). These results are mostly well known, but they are scattered in the literature - they are discussed in Chapter 1 (some with proof, others without proof, depending on the importance of the arguments in the proofs for later use and depending on the detail with which the results are discussed elsewhere in the literature) with the intention to provide an exposition which is mostly self contained and which will be comfortably accessible for graduate students. The dissertation reflects the outcome of our investigation in which we set ourselves the following goals: 1. Obtain a thorough understanding of the Dunford-Pettis property and some related (both weaker and stronger) properties that have been studied in the literature. 2. Focusing on the work in the paper [8], understand the role played in the study of difierent classes of operators by a scale of properties on Banach spaces, called the DPPp, which are weaker than the DP-property and which are introduced in [8] by using the weakly p-summable sequences in X and weakly null sequences in X*. 3. Focusing on the work in the paper [7], investigate the DP*P for Banach spaces, which is the exact property to answer a question of Pelczynsky's regarding when every symmetric bilinear separately compact map X x X  c0 is completely continuous. 4. Based on the ideas intertwined in the work of the paper [8] in the study of a scale of DP-properties and the work in the paper [7], introduce the DP*Pp on Banach spaces and investigate their applications to spaces of operators and in the theory of polynomials and analytic mappings on Banach spaces. Thereby, not only extending the results in [7] to a larger family of Banach spaces, but also to find an answer to the question: “When will every symmetric bilinear separately compact map X x X  c0 be p-convergent?"
Thesis (M.Sc. (Mathematics))--North-West University, Potchefstroom Campus, 2012.
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Maia, Mariana de Brito. "Um índice de somabilidade para operadores entre espaços de Banach." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9837.

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Nascimento, Lucas de Carvalho. "Um índice de somabilidade para pares de espaços de Banach." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9814.

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In this work, we study the notion of index of summability for pairs of Banach spaces. This index plays the role of a kind of “measure” of how the space of m-homogeneous polynomials from E to F (or the space of multilinear operators of E1×···×Em to F) are far from being the space of absolutely summing m-homogeneous polynomials (or with the space of multiple summing multilinear operators). In some cases the optimal index of summability is presented.
Neste trabalho, estudamos a noção de índice de somabilidade para pares de espaços de Banach. Esse índice desempenha o papel de um tipo de \medida" de como o espaço dos polinômios m-homogêneos de E em F (ou o espaço dos operadores multilineares de E Em em F) está longe de coincidir com o espaço dos polinômios m- homogêneos absolutamente somantes (ou com o espaço dos operadores multilineares multiplo somantes). Em alguns casos o índice ótimo de somabilidade e apresentado. Palavras-chave: Polinômios absolutamente somantes, operadores multilineares absolutamente somantes, espaços de Banach, índice de somabilidade.
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Santos, Lisiane Rezende dos. "Uma versão generalizada do Teorema de Extrapolação para operadores não-lineares absolutamente somantes." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9297.

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In this work we study a recent general version of the Extrapolation Theorem, due to Botelho, Pellegrino, Santos and Seoane-Sep ulveda [6] that improves and uni es a number of known Extrapolation-type theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators.
Neste trabalho, dissertamos sobre uma recente vers~ao geral do Teorema de Extrapola c~ao, devida a Botelho, Pellegrino, Santos e Seoane-Sep ulveda [6], que melhora e uni ca v arios teoremas do tipo Extrapola c~ao para certas classes de fun c~oes que generalizam o ideal dos operadores lineares absolutamente p-somantes.
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Books on the topic "Polynomials in Banach spaces"

1

Sarantopoulos, Ioannis C. Polynomials and multilinear mappings in Banach spaces. Uxbridge: Brunel University, 1986.

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Michal, Johanis, ed. Smooth analysis in Banach spaces. Berlin: De Gruyter, 2014.

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Kalton, Nigel J., and Elias Saab, eds. Banach Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074684.

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Lin, Bor-Luh, and William B. Johnson, eds. Banach Spaces. Providence, Rhode Island: American Mathematical Society, 1993. http://dx.doi.org/10.1090/conm/144.

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Ordered banach spaces. Paris: Hermann, 2008.

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E, Jamison James, ed. Isometries on Banach spaces: Function spaces. Boca Raton: Chapman & Hall/CRC, 2003.

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Wojtaszczyk, P. Banach spaces for analysts. Cambridge: Cambridge University Press, 1991.

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Hytönen, Tuomas, Jan van Neerven, Mark Veraar, and Lutz Weis. Analysis in Banach Spaces. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69808-3.

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Ledoux, Michel, and Michel Talagrand. Probability in Banach Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-20212-4.

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Hytönen, Tuomas, Jan van Neerven, Mark Veraar, and Lutz Weis. Analysis in Banach Spaces. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-48520-1.

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Book chapters on the topic "Polynomials in Banach spaces"

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Sundaresan, K. "Geometry of spaces of homogeneous polynomials on Banach lattices." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 571–86. Providence, Rhode Island: American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/004/43.

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Wojtaszczyk, P. "Some remarks about the space of measures with uniformly bounded partial sums and Banach-Mazur distances between some spaces of polynomials." In Lecture Notes in Mathematics, 60–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0090212.

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Komornik, Vilmos. "Banach Spaces." In Lectures on Functional Analysis and the Lebesgue Integral, 55–117. London: Springer London, 2016. http://dx.doi.org/10.1007/978-1-4471-6811-9_2.

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Brokate, Martin, and Götz Kersting. "Banach Spaces." In Compact Textbooks in Mathematics, 153–67. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15365-0_13.

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Kubrusly, Carlos S. "Banach Spaces." In Elements of Operator Theory, 197–309. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4757-3328-0_4.

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Lang, Serge. "Banach Spaces." In Real and Functional Analysis, 65–94. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0897-6_4.

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Pedersen, Gert K. "Banach Spaces." In Analysis Now, 43–78. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-1007-8_2.

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Farenick, Douglas. "Banach Spaces." In Fundamentals of Functional Analysis, 165–213. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45633-1_5.

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Denkowski, Zdzisław, Stanisław Migórski, and Nikolas S. Papageorgiou. "Banach Spaces." In An Introduction to Nonlinear Analysis: Theory, 255–403. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4419-9158-4_3.

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Siddiqi, Abul Hasan. "Banach Spaces." In Functional Analysis and Applications, 15–69. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-10-3725-2_2.

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Conference papers on the topic "Polynomials in Banach spaces"

1

Xiao, Xuemei, Xincun Wang, and Yucan Zhu. "Duality principles in Banach spaces." In 2010 3rd International Congress on Image and Signal Processing (CISP). IEEE, 2010. http://dx.doi.org/10.1109/cisp.2010.5648102.

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Kopecká, Eva, and Simeon Reich. "Nonexpansive retracts in Banach spaces." In Fixed Point Theory and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc77-0-12.

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Todorov, Vladimir T., and Michail A. Hamamjiev. "Transitive functions in Banach spaces." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’16): Proceedings of the 42nd International Conference on Applications of Mathematics in Engineering and Economics. Author(s), 2016. http://dx.doi.org/10.1063/1.4968490.

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Schroder, Matthias, and Florian Steinberg. "Bounded time computation on metric spaces and Banach spaces." In 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2017. http://dx.doi.org/10.1109/lics.2017.8005139.

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Baratella, S., and S. A. Ng. "MODEL-THEORETIC PROPERTIES OF BANACH SPACES." In Third Asian Mathematical Conference 2000. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777461_0004.

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González, Manuel. "Banach spaces with small Calkin algebras." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-10.

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Bamerni, Nareen, and Adem Kılıçman. "k-diskcyclic operators on Banach spaces." In INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4952536.

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GAO, SU. "EQUIVALENCE RELATIONS AND CLASSICAL BANACH SPACES." In Proceedings of the 9th Asian Logic Conference. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772749_0007.

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Zhang, Haizhang, Yuesheng Xu, and Jun Zhang. "Reproducing kernel Banach spaces for machine learning." In 2009 International Joint Conference on Neural Networks (IJCNN 2009 - Atlanta). IEEE, 2009. http://dx.doi.org/10.1109/ijcnn.2009.5179093.

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Develi, Faruk, and İsa Yıldırım. "Fixed point results in cone Banach spaces." In 7TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5078462.

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Reports on the topic "Polynomials in Banach spaces"

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Temlyakov, V. N. Greedy Algorithms in Banach Spaces. Fort Belvoir, VA: Defense Technical Information Center, January 2000. http://dx.doi.org/10.21236/ada637095.

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Yamamoto, Tetsuro. A Convergence Theorem for Newton's Method in Banach Spaces. Fort Belvoir, VA: Defense Technical Information Center, October 1985. http://dx.doi.org/10.21236/ada163625.

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Rosinski, J. On Stochastic Integral Representation of Stable Processes with Sample Paths in Banach Spaces. Fort Belvoir, VA: Defense Technical Information Center, January 1985. http://dx.doi.org/10.21236/ada152927.

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