G-frame representation and Invertibility of g-Bessel Multipliers
Abstract
In this paper we show that every g-frame for an infinite dimensional Hilbert space H can be written as a sum of three g-orthonormal bases for 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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