Perturbations of Operator Banach frames in Banach spaces

Authors

  • Chander Shekhar Department of Mathematics, Indraprastha college for Women, University of Delhi, Delhi 110007, INDIA
  • Shiv Kumar Kaushik Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110 007, INDIA

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.

 

Downloads

Published

2012-12-22

How to Cite

Shekhar, C., & Kaushik, S. K. (2012). Perturbations of Operator Banach frames in Banach spaces. Armenian Journal of Mathematics, 8(2), 104-119. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/128

Issue

Section

Articles