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arXiv · 1106.2139

G-frame representation and Invertibility of g-Bessel Multipliers

A. Abdollahi·E. Rahimi
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Abstract

In this paper we show that every g-frame for an \linebreak infinite dimensional Hilbert space $\mathcal{H}$ can be written as a sum of three g-orthonormal bases for $\mathcal{H}$. Also, we prove that every g-frame can be represented as a linear combination of two g-orthonormal bases if and only if it is a g-Riesz basis. Further, we show each g-Bessel multiplier is a Bessel multiplier and investigate the inversion of g-frame multipliers. Finally, we introduce the concept of controlled g-frames and weighted g-frames and show that the sequence induced by each controlled g-frame (resp. weighted g-frame) is a controlled frame (resp. weighted frame).

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BibTeXRIS

A. Abdollahi, E. Rahimi. 2011-06-10. G-frame representation and Invertibility of g-Bessel Multipliers. https://arxiv.org/abs/1106.2139

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