Armenian Journal of Mathematics, 8(2)
2012; 104–119
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Perturbations of Operator Banach frames inBanach spaces

Chander Shekhar*, Shiv Kumar Kaushik

Received: 2024-12-18 · Published: 2012-12-22

© 2012 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Perturbations of Operator Banach frames inBanach spaces
Authors
Chander Shekhar, Shiv Kumar Kaushik
Source journal
Armenian Journal of Mathematics, 8(2)
Published
2012-12-22
Licence
Creative Commons Attribution 4.0 International
Original
https://armjmath.sci.am/index.php/ajm/article/view/128

Abstract

Casazza and Christensen [3] studied perturbationof operators in the context of frames.Also, Chistensenand Heil [6] studied perturbation of frames and atomicdecompositions. In the present paper, we study perturbation ofoperator Banach frames (OBFs) for Banach spaces and obtainedperturbation results for operator Banach frames and operatorBessel sequences. Also, we give a condition under which thesum of finite number of sequences of operators is an OBF bycomparing each of the sequences with another system of OBFs.Finally, we define similar OBFs and prove that if a sequence ofoperators is similar to an OBF, then it has to be an OBF.
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