Sum Of K-Frames In Hilbert $C^{*}$-Modules

Abstract

In this paper, we investigate some conditions under which the action of an operator on a $K$-frame, remain again a $K$-frame for Hilbert module E. We also give a generalization of Douglas theorem to prove that the sum of two $K$-frames under certain condition is again a $K$-frame. Finally, we characterize the $K$-frame generators for a unitary system in terms of operators.