*-frames for operators on Hilbert modules

Document Type: Research Paper


Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran


$K$-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.


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