*-frames for operators on Hilbert modules

$K$-frames which are generalization of frames on Hilbert spacesý, ýwere introducedý ýto study atomic systems with respect to a bounded linear operatorý. ýIn this paperý, ý$*$-$K$-frames on Hilbert $C^*$-modulesý, ýas a generalization of $K$-framesý, ýare introduced and some of their properties are obtainedý. ýThen some relationsý ýbetween $*$-$K$-frames and $*$-atomic systems with respect to an adjointable operator are considered and some characterizations of $*$-$K$-frames are givený. ýFinally perturbations of $*$-$K$-frames are discussedý.