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.
Publisher
Universitat Politecnica de Valencia
Reference41 articles.
1. Y. A. Abramovich and C. D. Aliprantis, An Invitation to Operator Theory, Graduate Studies in Mathematics vol. 50, American Math. Soc., Providence, 2002. https://doi.org/10.1090/gsm/050
2. R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii, Measure of noncompactness and condensing operators,Birkhäuser Verlag Basel, 1992. https://doi.org/10.1007/978-3-0348-5727-7
3. A .G. Aksoy and J. M. Almira, On approximation schemes and compactness, Proceedings of the first conference on classical and functional analysis, Azuga-Romania (2014), 5-24.
4. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
5. J. Appell, Measure of noncompactness and some applications, Fixed Point Theory 6 (2005), 157-229.
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