*-Frames for operators on Hilbert modules

Abstract

K-frames were introduced by L. Gavruta to study atomic systems on Hilbert spaces. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper *-K-frames are introduced and some properties of this generalization of K-frames are studied. After proving some characterizations of *-K-frames, direct sum and tensor product of *-K-frames are considered and finally some perturbation results are established.