Bulletin of the
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Bull. Korean Math. Soc. 2021; 58(2): 461-479

Online first article March 4, 2021      Printed March 31, 2021

https://doi.org/10.4134/BKMS.b200358

Copyright © The Korean Mathematical Society.

Invertibility of generalized Bessel multipliers in Hilbert $C^{*}$-modules

Gholamreza Abbaspour Tabadkan, Hessam Hosseinnezhad

Damghan University; Damghan University

Abstract

This paper includes a general version of Bessel multipliers in Hilbert $C^*$-modules. In fact, by combining analysis, an operator on the standard Hilbert $C^*$-module and synthesis, we reach so-called generalized Bessel multipliers. Because of their importance for applications, we are interested to determine cases when generalized multipliers are invertible. We investigate some necessary or sufficient conditions for the invertibility of such operators and also we look at which perturbation of parameters preserve the invertibility of them. Subsequently, our attention is on how to express the inverse of an invertible generalized frame multiplier as a multiplier. In fact, we show that for all frames, the inverse of any invertible frame multiplier with an invertible symbol can always be represented as a multiplier with an invertible symbol and appropriate dual frames of the given ones.

Keywords: Bessel multiplier, modular Riesz basis, standard frame

MSC numbers: Primary 42C15, 46L08

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