Armenian Journal of Mathematics, 2(4)
2009; 146–154
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On k -deficit Banach Frames. Armenian Journal of Mathematics

Raj Kumar*, S. K. Kaushik

Received: 2024-12-20 · Published: 2009-12-29

© 2009 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
On k -deficit Banach Frames. Armenian Journal of Mathematics
Authors
Raj Kumar, S. K. Kaushik
Source journal
Armenian Journal of Mathematics, 2(4)
Published
2009-12-29
Licence
Creative Commons Attribution 4.0 International
Original
https://armjmath.sci.am/index.php/ajm/article/view/62

Abstract

kk-deficit Banach frames have been defined and studied. It has been proved that if a Banach space has a Banach frame having mbox{kk-deficit} (k≥0)(k≥0), then its second conjugate space has a retro Banach frame. Also, we prove results regarding existence of mbox{kk-deficit} Banach frames in subspaces and super spaces of a Banach space and deduce that ℓ∞ℓ∞ does not have a mbox{kk-deficit} Banach frame for any kk. Finally, we prove the equivalence of two statements regarding Banach frames.
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