G-frames as Sums of Some g-orthonormal Bases

• Journal title : Kyungpook mathematical journal
• Volume 53, Issue 1,  2013, pp.135-141
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2013.53.1.135
Title & Authors
G-frames as Sums of Some g-orthonormal Bases

Abstract
In this paper we show that a $\small{g}$-frame for a Hilbert space $\small{\mathcal{H}}$ can be written as a linear combination of two $\small{g}$-orthonormal bases for $\small{\mathcal{H}}$ if and only if it is a $\small{g}$-Riesz basis for $\small{\mathcal{H}}$. Also, we show that every $\small{g}$-frame for a Hilbert space $\small{\mathcal{H}}$ is a multiple of a sum of three $\small{g}$-orthonormal bases for $\small{\mathcal{H}}$.
Keywords
g-Bessel sequence;g-frame;g-orthonormal basis;g-Riesz basis;
Language
English
Cited by
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