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Статті в журналах з теми "Hilbert spaces"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 25 липня 2025

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1

Bellomonte, Giorgia, and Camillo Trapani. "Rigged Hilbert spaces and contractive families of Hilbert spaces." Monatshefte für Mathematik 164, no. 3 (2010): 271–85. http://dx.doi.org/10.1007/s00605-010-0249-1.

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2

CHITESCU, ION, RAZVAN-CORNEL SFETCU, and OANA COJOCARU. "Kothe-Bochner spaces that are Hilbert spaces." Carpathian Journal of Mathematics 33, no. 2 (2017): 161–68. http://dx.doi.org/10.37193/cjm.2017.02.03.

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Анотація:

We are concerned with Kothe-Bochner spaces that are Hilbert spaces (resp. hilbertable spaces). It is shown that ¨ this is equivalent to the fact that, separately, Lρ and X are Hilbert spaces (resp. hilbertable spaces). The complete characterization of the Lρ spaces that are Hilbert spaces, given by the first-author, is used.

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3

Sharma, Sumit Kumar, and Shashank Goel. "Frames in Quaternionic Hilbert Spaces." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 3 (2019): 395–411. http://dx.doi.org/10.15407/mag15.03.395.

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4

Sánchez, Félix Cabello. "Twisted Hilbert spaces." Bulletin of the Australian Mathematical Society 59, no. 2 (1999): 177–80. http://dx.doi.org/10.1017/s0004972700032792.

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A Banach space X is called a twisted sum of the Banach spaces Y and Z if it has a subspace isomorphic to Y such that the corresponding quotient is isomorphic to Z. A twisted Hilbert space is a twisted sum of Hilbert spaces. We prove the following tongue-twister: there exists a twisted sum of two subspaces of a twisted Hilbert space that is not isomorphic to a subspace of a twisted Hilbert space. In other words, being a subspace of a twisted Hilbert space is not a three-space property.

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5

Pisier, Gilles. "Weak Hilbert Spaces." Proceedings of the London Mathematical Society s3-56, no. 3 (1988): 547–79. http://dx.doi.org/10.1112/plms/s3-56.3.547.

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6

Fabian, M., G. Godefroy, P. Hájek, and V. Zizler. "Hilbert-generated spaces." Journal of Functional Analysis 200, no. 2 (2003): 301–23. http://dx.doi.org/10.1016/s0022-1236(03)00044-2.

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7

Rudolph, Oliver. "Super Hilbert Spaces." Communications in Mathematical Physics 214, no. 2 (2000): 449–67. http://dx.doi.org/10.1007/s002200000281.

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8

Ng, Chi-Keung. "Topologized Hilbert spaces." Journal of Mathematical Analysis and Applications 418, no. 1 (2014): 108–20. http://dx.doi.org/10.1016/j.jmaa.2014.03.073.

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9

van den Boogaart, Karl Gerald, Juan José Egozcue, and Vera Pawlowsky-Glahn. "Bayes Hilbert Spaces." Australian & New Zealand Journal of Statistics 56, no. 2 (2014): 171–94. http://dx.doi.org/10.1111/anzs.12074.

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10

Schmitt, L. M. "Semidiscrete Hilbert spaces." Acta Mathematica Hungarica 53, no. 1-2 (1989): 103–7. http://dx.doi.org/10.1007/bf02170059.

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11

Hollstein, Ralf. "Generalized Hilbert spaces." Results in Mathematics 8, no. 2 (1985): 95–116. http://dx.doi.org/10.1007/bf03322662.

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12

R.Kider, Jehad, and Ragahad Ibrahaim Sabre. "Fuzzy Hilbert Spaces." Engineering and Technology Journal 28, no. 9 (2010): 1816–24. http://dx.doi.org/10.30684/etj.28.9.10.

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13

Narita, Keiko, Noboru Endou, and Yasunari Shidama. "The Orthogonal Projection and the Riesz Representation Theorem." Formalized Mathematics 23, no. 3 (2015): 243–52. http://dx.doi.org/10.1515/forma-2015-0020.

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Анотація:

Abstract In this article, the orthogonal projection and the Riesz representation theorem are mainly formalized. In the first section, we defined the norm of elements on real Hilbert spaces, and defined Mizar functor RUSp2RNSp, real normed spaces as real Hilbert spaces. By this definition, we regarded sequences of real Hilbert spaces as sequences of real normed spaces, and proved some properties of real Hilbert spaces. Furthermore, we defined the continuity and the Lipschitz the continuity of functionals on real Hilbert spaces. Referring to the article [15], we also defined some definitions on

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14

Ciurdariu, Loredana. "Inequalities for selfadjoint operators on Hilbert spaces and pseudo-Hilbert spaces." Applied Mathematical Sciences 9 (2015): 5573–82. http://dx.doi.org/10.12988/ams.2015.56459.

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15

Mikhailets, Vladimir A., and Aleksandr A. Murach. "Interpolation Hilbert Spaces Between Sobolev Spaces." Results in Mathematics 67, no. 1-2 (2014): 135–52. http://dx.doi.org/10.1007/s00025-014-0399-x.

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16

Ismagilov, R. S. "Ultrametric spaces and related Hilbert spaces." Mathematical Notes 62, no. 2 (1997): 186–97. http://dx.doi.org/10.1007/bf02355907.

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17

Ghosh, Prasenjit. "Construction of fusion frame in Cartesian product of two Hilbert spaces." Gulf Journal of Mathematics 11, no. 2 (2021): 53–64. http://dx.doi.org/10.56947/gjom.v11i2.539.

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Анотація:

We study the concept of fusion frame in Cartesian product of two Hilbert spaces as Cartesian product of two Hilbert spaces is again a Hilbert space and see that the Cartesian product of two fusion frames is also a fusion frame. The concept of fusion frame operator on Cartesian product of two Hilbert spaces is being given and results of it are being presented.A perturbation result on fusion frame in Cartesian product of two Hilbert spaces is being discussed.

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18

Reddy, G. Upender. "On the Properties of Frames in 2-Hilbert Spaces." Asian Research Journal of Mathematics 21, no. 4 (2025): 136–46. https://doi.org/10.9734/arjom/2025/v21i4916.

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Анотація:

2-frames in 2-Hilbert spaces are studied, and several related results are presented. A definition of a frame associated with a fixed element in 2-Hilbert spaces is introduced and illustrated through examples. Various properties of the corresponding frame operator are investigated. Furthermore, several results from the theory of frames in Hilbert spaces are extended to the setting of 2-Hilbert spaces.

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19

Kryukov, Alexey A. "Linear algebra and differential geometry on abstract Hilbert space." International Journal of Mathematics and Mathematical Sciences 2005, no. 14 (2005): 2241–75. http://dx.doi.org/10.1155/ijmms.2005.2241.

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Isomorphisms of separable Hilbert spaces are analogous to isomorphisms ofn-dimensional vector spaces. However, whilen-dimensional spaces in applications are always realized as the Euclidean spaceRn, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. Images of charts on manifolds in the formalism are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations then describe families of functional

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20

Ghosh, Prasenjit, and Tapas Kumar Samanta. "Continuous frames in n-Hilbert spaces and their tensor products." Annals of the University of Craiova Mathematics and Computer Science Series 50, no. 1 (2023): 116–35. http://dx.doi.org/10.52846/ami.v50i1.1637.

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Анотація:

We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept of continuous frame for the tensor products of n-Hilbert spaces. Further, we study dual continuous frame and continuous Bessel multiplier in n-Hilbert spaces and their tensor products.

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21

Hong, Guoqing, and Pengtong Li. "Some Properties of Operator Valued Frames in Quaternionic Hilbert Spaces." Mathematics 11, no. 1 (2022): 188. http://dx.doi.org/10.3390/math11010188.

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Анотація:

Quaternionic Hilbert spaces play an important role in applied physical sciences especially in quantum physics. In this paper, the operator valued frames on quaternionic Hilbert spaces are introduced and studied. In terms of a class of partial isometries in the quaternionic Hilbert spaces, a parametrization of Parseval operator valued frames is obtained. We extend to operator valued frames many of the properties of vector frames on quaternionic Hilbert spaces in the process. Moreover, we show that all the operator valued frames can be obtained from a single operator valued frame. Finally, sever

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22

Faried, Nashat, Mohamed S.S. Ali, and Hanan H. Sakr. "Fuzzy soft Hilbert spaces." Journal of Mathematics and Computer Science 22, no. 02 (2020): 142–57. http://dx.doi.org/10.22436/jmcs.022.02.06.

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23

Marmo, G., A. Simoni, and F. Ventriglia. "Tomography in Hilbert spaces." Journal of Physics: Conference Series 87 (November 1, 2007): 012013. http://dx.doi.org/10.1088/1742-6596/87/1/012013.

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24

Preiss, David. "TILINGS OF HILBERT SPACES." Mathematika 56, no. 2 (2010): 217–30. http://dx.doi.org/10.1112/s0025579310000562.

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25

Hausenblas, Erika, and Markus Riedle. "Copulas in Hilbert spaces." Stochastics 89, no. 1 (2016): 222–39. http://dx.doi.org/10.1080/17442508.2016.1158821.

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26

Robertson, A. Guyan. "Injective matricial Hilbert spaces." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 1 (1991): 183–90. http://dx.doi.org/10.1017/s0305004100070237.

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Анотація:

Injective matricial operator spaces have been classified up to Banach space isomorphism in [20]. The result is that every such space is isomorphic to l∞, l2, B(l2), or a direct sum of such spaces. A more natural project, given the matricial nature of the definitions involved, would be the classification of such spaces up to completely bounded isomorphism. This was done for injective von Neumann algebras in [6] and for injective operator systems (i.e. unital injective operator spaces) in [19]. It turns out that the spaces l∞ and B(l2) are in a natural way uniquely characterized up to completely

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27

Bestvina, Mladen. "Stabilizing fake Hilbert spaces." Topology and its Applications 26, no. 3 (1987): 293–305. http://dx.doi.org/10.1016/0166-8641(87)90050-2.

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28

Dobrowolski, Tadeusz, and Janusz Grabowski. "Subgroups of Hilbert spaces." Mathematische Zeitschrift 211, no. 1 (1992): 657–69. http://dx.doi.org/10.1007/bf02571453.

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29

Ben-Yaacov, Itay, and Alexander Berenstein. "Imaginaries in Hilbert spaces." Archive for Mathematical Logic 43, no. 4 (2004): 459–66. http://dx.doi.org/10.1007/s00153-003-0200-4.

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30

Zerakidze, Z. S. "Hilbert spaces of measures." Ukrainian Mathematical Journal 38, no. 2 (1986): 131–35. http://dx.doi.org/10.1007/bf01058467.

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31

Gheondea, Aurelian. "On locally Hilbert spaces." Opuscula Mathematica 36, no. 6 (2016): 735. http://dx.doi.org/10.7494/opmath.2016.36.6.735.

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32

Sultanic, Saida. "Sub-Bergman Hilbert spaces." Journal of Mathematical Analysis and Applications 324, no. 1 (2006): 639–49. http://dx.doi.org/10.1016/j.jmaa.2005.12.035.

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33

Terekhin, P. A. "Multishifts in Hilbert spaces." Functional Analysis and Its Applications 39, no. 1 (2005): 57–67. http://dx.doi.org/10.1007/s10688-005-0017-5.

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34

HACIOGLU, EMIRHAN, та VATAN KARAKAYA. "Existence and convergence for a new multivalued hybrid mapping in CAT(κ) spaces". Carpathian Journal of Mathematics 33, № 3 (2017): 319–26. http://dx.doi.org/10.37193/cjm.2017.03.06.

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Анотація:

Most of the studies about hybrid mappings are carried out for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT (k) spaces which contains the multivalued generalization of (α, β) - hybrid mappings defined on Hilbert spaces. In this paper, we prove existence and convergence results for a new class of multivalued hybrid mappings on CAT(κ) spaces which are more general than Hilbert spaces and CAT(0) spaces.

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35

Hua, Dingli, and Yongdong Huang. "The Characterization and Stability of g-Riesz Frames for Super Hilbert Space." Journal of Function Spaces 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/465094.

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Анотація:

G-frames and g-Riesz frames as generalized frames in Hilbert spaces have been studied by many authors in recent years. The super Hilbert space has a certain advantage compared with the Hilbert space in the field of studying quantum mechanics. In this paper, for super Hilbert spaceH⊕K, the definitions of a g-Riesz frame and minimal g-complete are put forward; also a characterization of g-Riesz frames is obtained. In particular, we generalize them to general super Hilbert spaceL1⊕L2⊕⋯⊕Ln. Finally, a conclusion of the stability of a g-Riesz frame for the super Hilbert space is given.

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36

F. Al-Mayahi, Noori, and Abbas M. Abbas. "Some Properties of Spectral Theory in Fuzzy Hilbert Spaces." Journal of Al-Qadisiyah for computer science and mathematics 8, no. 2 (2017): 1–7. http://dx.doi.org/10.29304/jqcm.2016.8.2.27.

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Анотація:

In this paper we give some definitions and properties of spectral theory in fuzzy Hilbert spaces also we introduce definitions Invariant under a linear operator on fuzzy normed spaces and reduced linear operator on fuzzy Hilbert spaces and we prove theorms related to eigenvalue and eigenvectors ,eigenspace in fuzzy normed , Invariant and reduced in fuzzy Hilbert spaces and show relationship between them.

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37

GHOSH, PRASENJIT, and T. K. SAMANTA. "Fusion frame and its alternative dual in tensor product of Hilbert spaces." Creative Mathematics and Informatics 33, no. 1 (2024): 33–46. http://dx.doi.org/10.37193/cmi.2024.01.04.

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Анотація:

We study fusion frame in tensor product of Hilbert spaces and discuss some of its properties.\,The resolution of the identity operator on a tensor product of Hilbert spaces is being discussed.\,An alternative dual of a fusion frame in tensor product of Hilbert spaces is also presented.

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38

Solèr, M. P. "Characterization of hilbert spaces by orthomodular spaces." Communications in Algebra 23, no. 1 (1995): 219–43. http://dx.doi.org/10.1080/00927879508825218.

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39

NG, CHI-KEUNG. "On quaternionic functional analysis." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 2 (2007): 391–406. http://dx.doi.org/10.1017/s0305004107000187.

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Анотація:

AbstractIn this paper, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B*-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C*-algebras respectively. We will also give a Riesz representation theorem for quaternion Hilbert spaces and will extend the main results in [12] (namely, we will give the full versions of the Gelfand–Naimark theorem and the Gelfand theorem for quaternion B*-algebras). On our way to th

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40

Larionov, Evgeny. "ON STABILITY OF BASES IN HILBERT SPACES." Eurasian Mathematical Journal 11, no. 2 (2020): 65–71. http://dx.doi.org/10.32523/2077-9879-2020-11-2-65-71.

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41

Drahovský, Štefan, and Michal Zajac. "Hyperreflexive operators on finite dimensional Hilbert spaces." Mathematica Bohemica 118, no. 3 (1993): 249–54. http://dx.doi.org/10.21136/mb.1993.125929.

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42

Dixmier, Jacques. "Operateurs hypofermes." Journal of Operator Theory 91, no. 2 (2024): 323–33. https://doi.org/10.7900/jot.2023nov13.2451.

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Анотація:

Range spaces of bounded linear operators between Hilbert spaces, as well as linear operators between Hilbert spaces, whose graph is a bounded linear range of some Hilbert space, were systematically studied in an early paper. Here extensions of the above topics to the framework of general Banach spaces are discussed. A hypoclosed linear subspace of a Banach space is the range space of a bounded linear operator defined on some Banach space, while a hypoclosed linear operator is a linear operator between Banach spaces, whose graph is hypoclosed. Characterizations, permanence properties, pathologi

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43

Bayaz, Daraby, Delzendeh Fataneh, and Rahimi Asghar. "Parseval's equality in fuzzy normed linear spaces." MATHEMATICA 63 (86), no. 1 (2021): 47–57. http://dx.doi.org/10.24193/mathcluj.2021.1.05.

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Анотація:

We investigate Parseval's equality and define the fuzzy frame on Felbin fuzzy Hilbert spaces. We prove that C(Omega) (the vector space of all continuous functions on Omega) is normable in a Felbin fuzzy Hilbert space and so defining fuzzy frame on C(Omega) is possible. The consequences for the category of fuzzy frames in Felbin fuzzy Hilbert spaces are wider than for the category of the frames in the classical Hilbert spaces.

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44

Gao, Wen Hua, and Pei Xin Ye. "Estimates for Multilinear Hilbert Operators on Morrey Spaces and the Best Constants." Applied Mechanics and Materials 433-435 (October 2013): 531–34. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.531.

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45

Ghosh, Prasenjit. "Generalized fusion frame in quaternionic Hilbert spaces." Gulf Journal of Mathematics 16, no. 1 (2024): 123–35. http://dx.doi.org/10.56947/gjom.v16i1.1784.

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Анотація:

The notion of a generalized fusion frame in quaternionic Hilbert space is introduced. A characterization of generalized fusion frame in quaternionic Hilbert space with the help of frame operator is being discussed. Finally, g-fusion frame in quaternionic Hilbert space using invertible bounded right Q-linear operator on quaternionic Hilbert space is constructed.

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46

Ferrer, Osmin, Luis Lazaro, and Jorge Rodriguez. "Successions of J-bessel in Spaces with Indefinite Metric." WSEAS TRANSACTIONS ON MATHEMATICS 20 (April 6, 2021): 144–51. http://dx.doi.org/10.37394/23206.2021.20.15.

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Анотація:

A definition of Bessel’s sequences in spaces with an indefinite metric is introduced as a generalization of Bessel’s sequences in Hilbert spaces. Moreover, a complete characterization of Bessel’s sequences in the Hilbert space associated to a space with an indefinite metric is given. The fundamental tools of Bessel’s sequences theory are described in the formalism of spaces with an indefinite metric. It is shown how to construct a Bessel’s sequences in spaces with an indefinite metric starting from a pair of Hilbert spaces, a condition is given to decompose a Bessel’s sequences into in spaces

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47

Ghosh, Prasenjit, and T. K. Samanta. "Generalized Fusion Frame in A Tensor Product of Hilbert Space." Journal of the Indian Mathematical Society 89, no. 1-2 (2022): 58. http://dx.doi.org/10.18311/jims/2022/29307.

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Анотація:

Generalized fusion frames and some of their properties in a tensor product of Hilbert spaces are studied. Also, the canonical dual g-fusion frame in a tensor product of Hilbert spaces is considered. The frame operator for a pair of <em>g</em>-fusion Bessel sequences in a tensor product of Hilbert spaces is presented.

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48

Prykarpatskyy, Yarema A., Petro Ya Pukach, Myroslava I. Vovk, and Michal Greguš. "Some Remarks on Smooth Mappings of Hilbert and Banach Spaces and Their Local Convexity Property." Axioms 13, no. 4 (2024): 227. http://dx.doi.org/10.3390/axioms13040227.

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Анотація:

We analyze smooth nonlinear mappings for Hilbert and Banach spaces that carry small balls to convex sets, provided that the radii of the balls are small enough. We focus on the study of new and mildly sufficient conditions for the nonlinear mapping of Hilbert and Banach spaces to be locally convex, and address a suitably reformulated local convexity problem analyzed within the Leray–Schauder homotopy method approach for Hilbert spaces, and within the Lipschitz smoothness condition for both Hilbert and Banach spaces. Some of the results presented in this work prove to be interesting and novel,

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49

Guo, Xunxiang. "g-Bases in Hilbert Spaces." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/923729.

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Анотація:

The concept ofg-basis in Hilbert spaces is introduced, which generalizes Schauder basis in Hilbert spaces. Some results aboutg-bases are proved. In particular, we characterize theg-bases andg-orthonormal bases. And the dualg-bases are also discussed. We also consider the equivalent relations ofg-bases andg-orthonormal bases. And the property ofg-minimal ofg-bases is studied as well. Our results show that, in some cases,g-bases share many useful properties of Schauder bases in Hilbert spaces.

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50

Talakua, Mozart W., and Stenly J. Nanuru. "TEOREMA REPRESENTASI RIESZ–FRECHET PADA RUANG HILBERT." BAREKENG: Jurnal Ilmu Matematika dan Terapan 5, no. 2 (2011): 1–8. http://dx.doi.org/10.30598/barekengvol5iss2pp1-8.

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Анотація:

Hilbert space is a very important idea of the Davids Hilbert invention. In 1907, Riesz and Fréchet developed one of the theorem in Hilbert space called the Riesz-Fréchet representationtheorem. This research contains some supporting definitions Banach space, pre-Hilbert spaces, Hilbert spaces, the duality of Banach and Riesz-Fréchet representation theorem. On Riesz-Fréchet representation theorem will be shown that a continuous linear functional that exist in the Hilbert space is an inner product, in other words, there is no continuous linear functional on a Hilbert space except the inner produc

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