december 2022 Characterization and some properties of von Neumann-Schatten p-Bessel sequences
Farkhondeh Takhteh, Morteza Mirzaee Azandaryani
Bull. Belg. Math. Soc. Simon Stevin 29(3): 405-422 (december 2022). DOI: 10.36045/j.bbms.220511

Abstract

This paper considers von Neumann-Schatten p-Bessel sequences, von Neumann-Schatten p-frames and von Neumann-Schatten q-Riesz bases. Sequences, consisting of operators from a separable Banach space $\mathcal{X}$ into the von Neumann-Schatten p-class $\mathcal{C}_p$, which are von Neumann-Schatten p-Bessel sequences are characterized. It is shown that the set of all von Neumann-Schatten p-Bessel sequences can be considered as a Banach algebra. Also, some necessary and sufficient conditions for a reflexive Banach space to possess von Neumann-Schatten p-frames or von Neumann-Schatten q-Riesz bases are presented. Moreover, the stability of von Neumann-Schatten p-frames and von Neumann-Schatten q-Riesz bases under different kinds of perturbations is studied, especially some sufficient conditions for the preservation of the frame property under perturbations are derived.

Citation

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Farkhondeh Takhteh. Morteza Mirzaee Azandaryani. "Characterization and some properties of von Neumann-Schatten p-Bessel sequences." Bull. Belg. Math. Soc. Simon Stevin 29 (3) 405 - 422, december 2022. https://doi.org/10.36045/j.bbms.220511

Information

Published: december 2022
First available in Project Euclid: 22 March 2023

Digital Object Identifier: 10.36045/j.bbms.220511

Subjects:
Primary: 42C15 , 46C50

Keywords: Banach space , perturbation , von Neumann-Schatten p-Bessel sequence , von Neumann-Schatten p-frame , von Neumann-Schatten q-Riesz basis

Rights: Copyright © 2022 The Belgian Mathematical Society

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Vol.29 • No. 3 • december 2022
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