On The Frames In Hilbert $C^{\ast}$-modules

M'hamed Ghiati; Mohammed Mouniane; Mohamed Rossafi

On The Frames In Hilbert $C^{\ast}$-modules

Functional Analysis 2022-12-20 v1

Authors: M'hamed Ghiati , Mohammed Mouniane , Mohamed Rossafi

Abstract

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 in Hilbert $C^{\ast}$ -modules. Various proofs are given for some results. Also, we prove some new results. Moreover, non-trivial examples are presented.

Keywords

frame theory hilbert modules hilbert functions

Cite

@article{arxiv.2212.08940,
  title  = {On The Frames In Hilbert $C^{\ast}$-modules},
  author = {M'hamed Ghiati and Mohammed Mouniane and Mohamed Rossafi},
  journal= {arXiv preprint arXiv:2212.08940},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:1806.03993

On The Frames In Hilbert $C^{\ast}$-modules

Abstract

Keywords

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