The degree of nondensifiability of linear bounded operators and its applications

Gonzalo García; Gaspar Mora

doi:10.4995/agt.2024.19371

Authors

Gonzalo García National University of Distance Education https://orcid.org/0000-0001-6840-3226
Gaspar Mora Universidad Nacional de Asunción https://orcid.org/0000-0003-0883-220X

DOI:

https://doi.org/10.4995/agt.2024.19371

Keywords:

linear operators, compact operators, degree of nondensifiability, α -dense curves, Hyers-Ulam stability constant

Abstract

In the present paper we define the degree of nondensifiability (DND for short) of a bounded linear operator T on a Banach space and analyze its properties and relations with the Hausdorff measure of non-compactness (MNC for short) of T. As an application of our results, we have obtained a formula to find the essential spectral radius of a bounded operator T on a Banach space as well as we have provided the best possible lower bound for the Hyers-Ulam stability constant of T in terms of the aforementioned DND.

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