$*$-$K$-frames in Hilbert $C^*$-modules

Hosseini, Sedigheh

doi:10.30495/maca.2024.2045703.1112

$$-$K$-frames in Hilbert $C^$-modules

10.30495/maca.2024.2045703.1112

Volume 6, Issue 3
Autumn 2024

Pages 35-46

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Author

Sedigheh Hosseini

Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran

Abstract

In this paper, we introduce the concept of $*$-$K$-frames in Hilbert $C^*$-modules. We find a necessary and sufficient condition on a $*$-Bessel sequence to be a $*$-$K$-frame. Using the concept of $*$-$K$-frames, we show that an adjointable operator is surjective. Moreover, we prove that the image of a $*$-$K$-frame under the action of an operator remains again a $*$-$K$-frame for Hilbert $C^*$-module $\mathcal H$. In addition, we show that under what conditions an adjointable operator can be invertible.

Keywords

Frame

$*$-frame

$*$-$K$-frame

$C^*$-algebra

Hilbert $C^*$-module

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