Weaving Frames in Hilbert C ∗ -Modules

Abstract

In this paper, we investigate weaving frames in Hilbert $C^{\ast }$ -modules. We show that the equivalence of woven and weakly woven frames is still true for modular frames under certain conditions. By using the analysis operators of frames and frame operators of canonical duals, we obtain several perturbation results for given weaving frames and different weaving frame pairs. When the $C^{\ast }$ -algebra is nonunital, we derive a correspondence of adjointable operators which is bounded below woven families. Finally, we discuss the redundancy of weaving frames in Hilbert $C^{\ast }$ -modules.