On the frames in Hilbert $C^{\ast}$-modules

Journal of Linear and Topological Algebra

دوره 12، شماره 01، خرداد 2023، صفحه 1-32   

نوع مقاله: Review paper

شناسه دیجیتال (DOI): 10.30495/jlta.2023.1979703.1536

نویسندگان

M. Rossafi^{* 1}؛ M. Ghiati²؛ M. Mouniane²

¹LaSMA Laboratory, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco

²Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics, Ibn Tofail University, Kenitra, Morocco

چکیده

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.

کلیدواژه‌ها

Frame؛ $\ast$-frame؛ $g$-frame؛ $\ast$-$g$-frame؛ $\ast$-$K$-$g$-frame؛ operator frame؛ Hilbert $C^{\ast}$-modules

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