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Journal articles on the topic 'Hilbert spaces'

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Published: 4 June 2021

Last updated: 6 September 2023

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1

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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2

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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3

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.

4

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.

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

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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13

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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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

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.

16

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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17

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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18

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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19

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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20

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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21

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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22

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.

23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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.

31

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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32

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.

33

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.

34

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.

35

HACIOGLU, EMIRHAN, and VATAN KARAKAYA. "Existence and convergence for a new multivalued hybrid mapping in CAT(κ) spaces." Carpathian Journal of Mathematics 33, no. 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.

36

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.

37

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.

38

García-Pacheco, Francisco Javier, and Justin R. Hill. "Geometric Characterizations of Hilbert Spaces." Canadian Mathematical Bulletin 59, no. 4 (December 1, 2016): 769–75. http://dx.doi.org/10.4153/cmb-2016-019-8.

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AbstractWe study some geometric properties related to the setobtaining two characterizations of Hilbert spaces in the category of Banach spaces. We also compute the distance of a generic element (h, k) ∊ for H a Hilbert space.

39

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.

40

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.

41

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.

42

Parsian, A., and A. Shafei Deh Abad. "Dirac structures on Hilbert spaces." International Journal of Mathematics and Mathematical Sciences 22, no. 1 (1999): 97–108. http://dx.doi.org/10.1155/s0161171299220972.

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For a real Hilbert space(H,〈,〉), a subspaceL⊂H⊕His said to be a Dirac structure onHif it is maximally isotropic with respect to the pairing〈(x,y),(x′,y′)〉+=(1/2)(〈x,y′〉+〈x′,y〉). By investigating some basic properties of these structures, it is shown that Dirac structures onHare in one-to-one correspondence with isometries onH, and, any two Dirac structures are isometric. It is, also, proved that any Dirac structure on a smooth manifold in the sense of [1] yields a Dirac structure on some Hilbert space. The graph of any densely defined skew symmetric linear operator on a Hilbert space is, also, shown to be a Dirac structure. For a Dirac structureLonH, everyz∈His uniquely decomposed asz=p1(l)+p2(l)for somel∈L, wherep1andp2are projections. Whenp1(L)is closed, for any Hilbert subspaceW⊂H, an induced Dirac structure onWis introduced. The latter concept has also been generalized.

43

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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44

Picard, Rainer H. "Hilbert spaces of tempered distributions, Hermite expansions and sequence spaces." Proceedings of the Edinburgh Mathematical Society 34, no. 2 (June 1991): 271–93. http://dx.doi.org/10.1017/s0013091500007173.

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Although it is well-known that tempered distributions on ℝn can be expanded into series of Herrnite functions, it does not seem to be known, however, that expansions of this type are accessible through the elementary concept of orthonorma! expansions in Hilbert space. This approach is developed here complementing previous work on a Hilbert space approach to distributions. The basis of the development is the observation that the Hermite functions are a complete orthogonal set in each space of a certain scale of Sobolev type Hilbert spaces associated with the family of differential operators defined byHere Ф denotes a smooth function with compact support. The setting is first developed in the one-dimensional case. By use of the usual multi-index notation this can be extended to the higher-dimensional case. As applications various imbedding results are derived. The paper concludes with a characterization of tempered distributions by convergent Hermite expansions.

45

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.

46

Kapustin, Vladimir. "Commutators on l2-spaces." Publications de l'Institut Math?matique (Belgrade) 97, no. 111 (2015): 125–37. http://dx.doi.org/10.2298/pim140205001k.

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Given a normal operator N on a Hilbert space and an operator X for which the commutator K = XN ?NX belongs to the Hilbert-Schmidt class, we discuss the possibility to represent X as a sum of a Cauchy transform corresponding to K in the spectral representation of N and an operator commuting with N.

47

Bozkurt, Hacer, Sümeyye Çakan, and Yılmaz Yılmaz. "Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces." International Journal of Analysis 2014 (March 11, 2014): 1–7. http://dx.doi.org/10.1155/2014/258389.

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Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals (Aseev (1986)). Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as (Rojas-Medar et al. (2005), Talo and Başar (2010), and Nikol'skiĭ (1993)). His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis.

48

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.

49

Al-Mayahi, Noori F., and Intisar H. Radhi. "On Fuzzy Co-Pre-Hilbert Spaces." Journal of Kufa for Mathematics and Computer 1, no. 7 (December 1, 2013): 1–6. http://dx.doi.org/10.31642/jokmc/2018/010701.

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50

Androulakis, George, Peter G. Casazza, and Denka N. Kutzarova. "Some More Weak Hilbert Spaces." Canadian Mathematical Bulletin 43, no. 3 (September 1, 2000): 257–67. http://dx.doi.org/10.4153/cmb-2000-033-0.

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