# Perturbations of Operator Banach frames in Banach spaces

Shekhar, Chander and Kaushik, Shiv Kumar (2016) Perturbations of Operator Banach frames in Banach spaces. Armenian Journal of Mathematics, 8 (2). pp. 104-119. ISSN 1829-1163

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## Abstract

Casazza and Christensen \cite{BB} studied perturbation of operators in the context of frames. Also, Chistensen and Heil \cite{DD} studied perturbation of frames and atomic decompositions. In the present paper, we study perturbation of operator Banach frames (OBFs) for Banach spaces and obtained perturbation results for operator Banach frames and operator Bessel sequences. Also, we give a condition under which the sum of finite number of sequences of operators is an OBF by comparing each of the sequences with another system of OBFs. Finally, we define similar OBFs and prove that if a sequence of operators is similar to an OBF, then it has to be an OBF.

Item Type: Article 42-xx Fourier analysis46-xx Functional analysis 672 Shiv Kumar KAAAUSHIK 22 Dec 2016 14:51 22 Dec 2016 14:51

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