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Zeitschriftenartikel zum Thema „Hilbert spaces“

Autor: Grafiati

Veröffentlicht am 4. Juni 2021

Zuletzt aktualisiert am 9. Juni 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 (October 8, 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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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 (June 25, 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 (April 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 (May 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 (June 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 (November 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 (October 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 (June 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 (March 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 (May 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 (April 1, 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 (September 1, 2015): 243–52. http://dx.doi.org/10.1515/forma-2015-0020.

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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 real Hilbert spaces and proved some theorems for defining dual spaces of real Hilbert spaces. As to the properties of all definitions, we proved that they are equivalent properties of functionals on real normed spaces. In Sec. 2, by the definitions [11], we showed properties of the orthogonal complement. Then we proved theorems on the orthogonal decomposition of elements of real Hilbert spaces. They are the last two theorems of existence and uniqueness. In the third and final section, we defined the kernel of linear functionals on real Hilbert spaces. By the last three theorems, we showed the Riesz representation theorem, existence, uniqueness, and the property of the norm of bounded linear functionals on real Hilbert spaces. We referred to [36], [9], [24] and [3] in the formalization.

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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 (July 11, 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 (August 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 (September 12, 2021): 53–64. http://dx.doi.org/10.56947/gjom.v11i2.539.

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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 (April 14, 2025): 136–46. https://doi.org/10.9734/arjom/2025/v21i4916.

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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 equations on various spaces of functions. The formalism itself and its applications in linear algebra, differential equations, and differential geometry are carefully analyzed.

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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 (June 30, 2023): 116–35. http://dx.doi.org/10.52846/ami.v50i1.1637.

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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 (December 29, 2022): 188. http://dx.doi.org/10.3390/math11010188.

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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, several results for operator valued frames concerning duality, similarity of such frames on quaternionic Hilbert spaces are presented.

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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 (July 18, 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 (April 29, 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 (March 16, 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 (July 1991): 183–90. http://dx.doi.org/10.1017/s0305004100070237.

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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 bounded isomorphism. However, as shown in [20], a problem arises in the case of l2. For there are two injective operator spaces which are each isometrically isomorphic to l2 but not completely boundedly isomorphic to each other. We shall resolve this problem by showing that these are the only two possibilities, in the sense that any injective operator space which is isometric to l2 is completely isometric to one of them. (See Corollary 3 below.) The Hilbert spaces in von Neumann algebras investigated in [17], [13] turn out to be injective matricial operator spaces and are therefore completely isometric to one of our two examples. Another Hilbert space in B(l2) which has been much studied in operator theory, complex analysis and physics is the Cartan factor of type IV [10]. This is the complex linear span of a spin system and generates the Fermion C*-algebra ([3], §5·2). We show that a Cartan factor of type IV is not even completely boundedly isomorphic to an injective matricial operator space. One curious property of all the aforementioned Hilbert spaces is that every bounded operator on them is actually completely bounded, a fact that is crucial in our proofs.

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27

Bestvina, Mladen. "Stabilizing fake Hilbert spaces." Topology and its Applications 26, no. 3 (August 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 (December 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 (May 1, 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 (December 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 (January 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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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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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 (August 7, 2017): 1–7. http://dx.doi.org/10.29304/jqcm.2016.8.2.27.

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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 (February 3, 2024): 33–46. http://dx.doi.org/10.37193/cmi.2024.01.04.

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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 (January 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 (September 2007): 391–406. http://dx.doi.org/10.1017/s0305004107000187.

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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 these results, we compare, clarify and unify the term ‘quaternion Hilbert spaces’ in the literatures.

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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 (May 2024): 323–33. https://doi.org/10.7900/jot.2023nov13.2451.

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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, pathologies are presented, and several significant differences to the Hilbert space case are emphasized.

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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 (May 20, 2021): 47–57. http://dx.doi.org/10.24193/mathcluj.2021.1.05.

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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 (March 8, 2024): 123–35. http://dx.doi.org/10.56947/gjom.v16i1.1784.

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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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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 with an indefinite metric so that this decomposition generates a pair of Bessel’s sequences for the Hilbert spaces corresponding to the fundamental decomposition. In spaces where there was no norm, it seemed impossible to construct Bessel’s sequences. The fact that in [1] frame were constructed for Krein spaces motivated us to construct Bessel’s sequences for spaces of indefinite metric.

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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 (January 27, 2022): 58. http://dx.doi.org/10.18311/jims/2022/29307.

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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 (March 29, 2024): 227. http://dx.doi.org/10.3390/axioms13040227.

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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, even for finite-dimensional problems. Open problems related to the local convexity property for nonlinear mappings of Banach spaces are also formulated.

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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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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

Jafari, F., and R. Raposa. "On cyclicity in weighted Dirichlet spaces." International Journal of Mathematics and Mathematical Sciences 22, no. 4 (1999): 739–44. http://dx.doi.org/10.1155/s0161171299227391.

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We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces0<α<1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.

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