Approximately Dual p-Approximate Schauder Frames

Krishna, K. Mahesh; Johnson, P. Sam

doi:10.48550/arxiv.2110.10121

Cited by 2 publications

(4 citation statements)

References 15 publications

(23 reference statements)

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“…In [29], it is also showed by Christensen and Laugesen that by perturbing frame we can get approximate duals. In [61], it is showed that this result is valid for Banach spaces. Here is the operator-valued version of that result.…”

Section: Approximate Dualitymentioning

confidence: 87%

“…In [29], Christensen and Laugesen gave a method to construct approximately duals iteratively. In [61], this result was derived for Banach spaces. Here we have a similar result for operator-valued p-ABSs.…”

Section: Approximate Dualitymentioning

confidence: 98%

“…This led Christensen and Laugesen [29] to introduce the notion of approximate duals (also see [70]). This notion has then been introduced and characterized for Banach spaces in [61]. Here we give operator-valued version of those results for Banach spaces.…”

Section: Approximate Dualitymentioning

confidence: 99%

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Operator-Valued p-Approximate Schauder Frames

Krishna¹,

Johnson²

2022

Preprint

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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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Section: Approximate Dualitymentioning

confidence: 87%

Section: Approximate Dualitymentioning

confidence: 98%

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Operator-Valued p-Approximate Schauder Frames

Krishna¹,

Johnson²

2022

Preprint

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“…Definition 2.1. [82,84] Let p ∈ [1, ∞). Let {τ n } n be a sequence in a Banach space X and {f n } n be a sequence in X * (dual of X ).…”

Section: Introductionmentioning

confidence: 99%

Feichtinger Conjectures, $R_\varepsilon$-Conjectures and Weaver's Conjectures for Banach spaces

Krishna¹

2022

Preprint

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Motivated from two decades old famous Feichtinger conjectures for frames, R ε -conjecture and Weaver's conjecture for Hilbert spaces (and their solution by Marcus, Spielman, and Srivastava), we formulate Feichtinger conjectures for p-approximate Schauder frames, R ε -conjecture, Weaver's conjectures and Akemann-Weaver conjectures for Banach spaces. We also formulate conjectures on p-approximate Schauder frames based on the results of Casazza for frames for Hilbert spaces. We state conjectures and problems for p-approximate Schauder frames based on fundamental inequality for frames for Hilbert spaces and scaling problem for Hilbert space frames. Based on Kothe-Lorch theorem for Riesz bases for Hilbert spaces, we formulate a problem for p-approximate Riesz bases for Banach spaces. We formulate dynamical sampling problem for p-approximate Schauder frames for Banach spaces. We ask phase retrieval problem and norm retrieval problem for p-approximate Schauder frames for Banach spaces. We also formulate discretization problem for continuous p-approximate Schauder frames.

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Approximately Dual p-Approximate Schauder Frames

Cited by 2 publications

References 15 publications

Operator-Valued p-Approximate Schauder Frames

Operator-Valued p-Approximate Schauder Frames

Feichtinger Conjectures, $R_\varepsilon$-Conjectures and Weaver's Conjectures for Banach spaces

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