Perturbations of Operator Banach frames inBanach spaces

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Submitted: 2024-12-18; Published: 2024-12-18

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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.