Bessel multipliers in Hilbert $C^\ast$--modules

Abstract

In this paper we introduce Bessel multipliers, g-Bessel multipliers and Bessel fusion multipliers in Hilbert $C^\ast$--modules and we show that they share many useful properties with their corresponding notions in Hilbert and Banach spaces. We show that various properties of multipliers are closely related to their symbols and Bessel sequences, especially we consider multipliers when their Bessel sequences are modular Riesz bases and we see that in this case multipliers can be composed and inverted. We also study bounded below multipliers and generalize some of the results obtained for fusion frames in Hilbert spaces to Hilbert $C^\ast$--modules.