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[FORTHCOMING] A(n,m)-iso-contra-expansive operators and some applications on Bergman spaces

[FORTHCOMING] Les opérateurs A(n, m)-iso-contra-expansifs et quelques applications sur les espaces de Bergman


Gherairi Khadija
University of Gabès
Tunisia

Sedki Amira
University of Jendouba
Tunisia

Snoun Safa
University of Gabès
Tunisia



Validated on 20 January 2025   DOI : TBA

Abstract

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In this paper, we study a new class of operators, so called $$$A(n,m)$$$-iso-contra-expansive operators. These new families of operators are considered as a generalization that combines the $$$m$$$-expansive operators as well as m-contractive operators and the classes of $$$(A,m)$$$-expansive and $$$(A,m)$$$-contractive operators and we recover the notion of $$$n$$$-quasi-$$$(A,m)$$$-isometric operators. Some spectral properties of these kind of operators are provided, we derive also a conditions to have the single-valued extension property (SVEP) and we finish by an application of Toeplitz operators on Bergman spaces.

In this paper, we study a new class of operators, so called $$$A(n,m)$$$-iso-contra-expansive operators. These new families of operators are considered as a generalization that combines the $$$m$$$-expansive operators as well as m-contractive operators and the classes of $$$(A,m)$$$-expansive and $$$(A,m)$$$-contractive operators and we recover the notion of $$$n$$$-quasi-$$$(A,m)$$$-isometric operators. Some spectral properties of these kind of operators are provided, we derive also a conditions to have the single-valued extension property (SVEP) and we finish by an application of Toeplitz operators on Bergman spaces.

Bergman spaces Toeplitz operators m-contractive m-expansive

Bergman spaces Toeplitz operators m-contractive m-expansive