On Controlled Frames in Hilbert $C^{\ast }$-modules

Abstract

In this paper, we introduce controlled frames in Hilbert $C^{\ast }$-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. Next, we give a characterization of controlled frames in Hilbert $C^{\ast }$-module. Also multiplier operators for controlled frames in Hilbert $C^{\ast }$-modules will be defined and some of its properties will be shown. Finally, we investigate weighted frames in Hilbert $C^{\ast }$-modules and verify their relations to controlled frames and multiplier operators.