In this article, we introduce the concept of generalized multipliers for g-frames. In fact, we show that every generalized multiplier for g-Bessel sequences is a generalized multiplier for the induced sequences, in a special sense. We provide some sufficient and/or necessary conditions for the invertibility of generalized multipliers. In particular, we characterize g-Riesz bases by invertible multipliers. We look at which perturbations of g-Bessel sequences preserve the invertibility of generalized multipliers. Finally, we investigate how to find a matrix representation of operators on a Hilbert space using g-frames, and then we characterize g-Riesz bases and g-orthonormal bases by applying such matrices.
"G-frames and their generalized multipliers in Hilbert spaces." Ann. Funct. Anal. 10 (2) 180 - 195, May 2019. https://doi.org/10.1215/20088752-2018-0017