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Asghar Rahimi

Asghar Rahimi

Academic rank: Professor
ORCID:
Education: PhD.
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Faculty: 1
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Research

Title
Generalized Bessel Multipliers in Hilbert Spaces
Type
JournalPaper
Keywords
Bessel sequence, frame, Bessel multipliers, Riesz basis
Year
2018
Journal Results in Mathematics
DOI
Researchers Golamreza Abbaspour Tabadkan ، Hessam Hosseinnezhad ، Asghar Rahimi

Abstract

The notation of generalized Bessel multipliers is obtained by a bounded operator on 2 which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to their parameters, in particular, it will be shown that the membership of generalized Bessel multiplier in the certain operator classes requires that its symbol belongs in the same classes, in a special sense. Also, we give some examples to illustrate our results. As we shall see, generalized multipliers associated with Riesz bases are well-behaved, more precisely in this case multipliers can be easily composed and inverted. Special attention is devoted to the study of invertible generalized multipliers. Sufficient and/or necessary conditions for invertibility are determined. Finally, the behavior of these operators under perturbations is discussed.