The degree of nondensifiability of linear bounded operators and its applications

• García, Gonzalo ^[1] ; Mora, Gaspar ^[2]
  1. [1] Universidad Nacional de Educación a Distancia

     Universidad Nacional de Educación a Distancia

     Madrid, España

     
  2. [2] Universidad Nacional de Asunción

     Universidad Nacional de Asunción

     Paraguay

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 1, 2024, págs. 213-228
• Idioma: inglés
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• Resumen

  • 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.