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 gframe 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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