# On $\bm{k}$-deficit Banach Frames

Kaushik, S. K. and Kumar, Raj (2009) On $\bm{k}$-deficit Banach Frames. Armenian Journal of Mathematics, 2 (4). pp. 146-154. ISSN 1829-1163

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## Abstract

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

Item Type: Article 42-xx Fourier analysis 192 Professor Anry Nersesyan 29 Dec 2009 17:21 19 Apr 2011 02:23

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