Paulsen and Projection Problems for Banach Spaces

Krishna, K. Mahesh

doi:10.48550/arxiv.2201.00991

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Operator-valued Feichtinger Conjectures1

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2022

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Cited by 2 publications

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“…After the solution of Paulsen problem (and hence projection problem), both Paulsen and projection problems are stated for Banach spaces which is open till today [69]. In this paper, we formulate Paulsen and projection problems for Hilbert C*-modules based on frame theory for Hilbert C*-modules.…”

Section: Hsmentioning

confidence: 99%

Modular Paulsen Problem and Modular Projection Problem

Krishna¹

2022

Preprint

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Based on the solution of Paulsen Problem by Kwok, Lau, Lee, and Ramachandran [STOC'18-Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, 2018 ] and independently by Hamilton, and Moitra [Isr. J. Math., 2021 ] we study Paulsen Problem and Projection Problem in the context of Hilbert C*-modules. We show that for commutative C*-algebras, if Modular Paulsen Problem has a solution, then Modular Projection Problem also has a solution. We formulate the problem of operator scaling for matrices over C*-algebras.

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Section: Hsmentioning

confidence: 99%

Modular Paulsen Problem and Modular Projection Problem

Krishna¹

2022

Preprint

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“…Recently first author formulated a variety of conjectures and problems for p-approximate Schauder frames for Banach spaces [59,60]. Here we present operator-valued versions of some of them.…”

Section: Operator-valued Feichtinger Conjecturesmentioning

confidence: 99%

Operator-Valued p-Approximate Schauder Frames

Krishna¹,

Johnson²

2022

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We give an operator-algebraic treatment of theory of p-approximate Schuader frames which includes the theory of operator-valued frames by Kaftal, Larson, and Zhang [Trans. AMS., 2009 ], Gframes by Sun [JMAA, 2006], factorable weak operator-valued frames by Krishna and Johnson [Annals of FA, 2022 ] and p-approximate Schauder frames by Krishna and Johnson [J. Pseudo-Differ. Oper. Appl, 2021 ] as particular cases. We show that a sufficiently rich theory can be developed even for Banach spaces. We achieve this by defining various concepts and characterizations in Banach spaces. These include duality, approximate duality, equivalence, orthogonality and stability.

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Paulsen and Projection Problems for Banach Spaces

Abstract: Based on the two decades old celebrated Paulsen problem and its solutions for Hilbert spaces by Kwok, Lau, Lee, Ramachandran, Hamilton, and Moitra, we formulate Paulsen problem for Banach spaces. We also formulate projection problem for Banach spaces.

Cited by 2 publications

References 20 publications

Modular Paulsen Problem and Modular Projection Problem

Modular Paulsen Problem and Modular Projection Problem

Operator-Valued p-Approximate Schauder Frames

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