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ON NEAR EXACT BANACH FRAMES IN BANACH SPACES

Part of: Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  01 October 2008

P. K. JAIN ,
S. K. KAUSHIK  and
NISHA GUPTA
P. K. JAIN
Affiliation:
Department of Mathematics, University of Delhi, Delhi 110 007, India (email: pawankrjain@yahoo.com)
S. K. KAUSHIK*
Affiliation:
Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110 007, India (email: shikk2003@yahoo.co.in)
NISHA GUPTA
Affiliation:
Department of Mathematics, University of Delhi, Delhi 110 007, India (email: nishag_81@yahoo.co.in)
*
✉For correspondence; e-mail: shikk2003@yahoo.co.in
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Abstract

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Near exact Banach frames are introduced and studied, and examples demonstrating the existence of near exact Banach frames are given. Also, a sufficient condition for a Banach frame to be near exact is obtained. Further, we consider block perturbation of retro Banach frames, and prove that a block perturbation of a retro Banach frame is also a retro Banach frame. Finally, it is proved that if E and F are both Banach spaces having Banach frames, then the product space E×F has an exact Banach frame.

Keywords

framesBanach framesretro Banach frames

MSC classification

Secondary: 42C15: General harmonic expansions, frames
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 335 - 342
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The research of the third author was supported by the Council of Scientific and Industrial Research (CSIR), India (vide letter no. 9/45(595)/2005-EMR-I dated 08.09.2005).

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