*-frames for operators on Hilbert modules

K-frames which are generalization of frames on Hilbert spaces‎, ‎were introduced‎ ‎to study atomic systems with respect to a bounded linear operator‎. ‎In this paper‎, ‎*-K-frames on Hilbert C^*-modules‎, ‎as a generalization of K-frames‎, ‎are introduced and some of their properties are obtained‎. ‎Then some relations‎ ‎between *-K-frames and *-atomic systems with respect to an adjointable operator are considered and some characterizations of *-K-frames are given‎. ‎Finally perturbations of *-K-frames are discussed‎.

Keywords:

K-framesep *-frame , Hilbert , C^*-module‎