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The degree of nondensifiability of linear bounded operators and its applications

    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.


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