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On The Frames In Hilbert $C^{\ast}$-modules (2212.08940v1)

Published 17 Dec 2022 in math.FA

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.