K-Frames in Super Hilbert C∗-Modules

Abstract

In this paper, we study the theory of K-frames in super Hilbert C∗-modules. We introduce the concept of super Hilbert modules as direct sums of Hilbert C∗-modules and explore how frames and K-frames can be defined and characterized within this framework. Our main results provide new characterizations of K-frames in super Hilbert C∗-modules, as well as necessary and sufficient conditions under which sequences in super Hilbert C∗-modules form K-frames. Additionally, we investigate the relationships between K-frames, minimal frames, and orthonormal bases, offering several propositions and illustrative examples. These findings extend the existing frame theory in Hilbert spaces to the richer structure of Hilbert C∗-modules, thereby contributing to a deeper understanding of operator theory and functional analysis in the context of C∗-algebras.