K-Frames in Super Hilbert C∗-Modules

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DOI: https://doi.org/10.28924/2291-8639-23-2025-19
Published: Jan 27, 2025
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Abdellatif Lfounoune, Roumaissae El Jazzar, K-Frames in Super Hilbert C∗-Modules, Int. J. Anal. Appl., 23 (2025), 19.

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Abdellatif Lfounoune, Roumaissae El Jazzar

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.

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