Invertibility of g-frame multipliers and Bessel multipliers for unitary systems in Hilbert C*-modules

Abstract

ABSTRACT In this paper, firstly we explore the invertibility of g-frame multipliers in Hilbert -modules. We show that for -invertible symbols, a modular g-Riesz multiplier is automatically invertible, and that the inverse of any invertible g-frame multiplier can be represented as a g-frame multiplier and particularly, we determine a new case of invertible g-frame multipliers whose inverses are exact the g-frame multipliers with the inverse of the symbol and the canonical dual g-frames. A necessary and sufficient condition for the invertibility of g-frame multipliers is obtained from the operator-theoretic point of view, and we also show that a small perturbation is applied to the g-frame involved in an invertible g-frame multiplier can lead to a new invertible g-frame multiplier. We end the paper by introducing what we call Bessel multipliers for unitary systems in Hilbert -modules and study their basic properties.