In this paper, we introduce the concepts of $\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modules and we establish some results. تفاصيل المقالة

‎Frames generalize orthonormal bases and allow representation of all the elements of the space‎. ‎Frames play significant role in signal and image processing‎, ‎which leads to many applications in informatics‎, ‎engineering‎, ‎medicine‎, ‎and probability‎. ‎In this paper‎, ‎we introduce the concepts of operator frame for the space $End_{\mathcal{A}}^{\ast}(\mathcal{H})$ of all adjointable operators on a Hilbert $\mathcal{A}$-module $\mathcal{H}$ and establish some results‎. تفاصيل المقالة

Frame theory has been rapidly generalized and various generalizations have been developed. In this paper, we present a brief survey of the frames in Hilbert $C^{\ast}$-modules, including frames, $\ast$-frames, g-frames, $\ast$-g-frames, $\ast$-$K$-$g$-frame, operator frame and $\ast$-$K$-operator frame in Hilbert $C^{\ast}$-modules. Various proofs are given for some results. We will also provide some new results. Moreover, non-trivial examples are presented. تفاصيل المقالة