On the frames in Hilbert $C^{\ast}$-modules
Subject Areas : Abstract harmonic analysis
M. Rossafi
1
,
M. Ghiati
2
,
M. Mouniane
3
1 - LaSMA Laboratory, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
2 - Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics, Ibn Tofail University, Kenitra, Morocco
3 - Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics, Ibn Tofail University, Kenitra, Morocco
Keywords: Frame, operator frame, $g$-frame, $\ast$-frame, $\ast$-$g$-frame, $\ast$-$K$-$g$-frame, Hilbert $C^{\ast}$-modules,
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 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.
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