Invertibility of multipliers in Hilbert C*-modules

Abstract

In this paper, we present some sufficient conditions under which Bessel multipliers in Hilbert C*-modules with semi-normalized symbols are invertible and we calculate the inverses. Especially we consider the invertibility of Bessel multipliers when the elements of their symbols are positive and when their Bessel sequences are equivalent, duals, modular Riesz bases or stable under small perturbations. We show that in these cases the inverse of a Bessel multiplier can be represented as a Bessel multiplier.