The degree of nondensifiability of linear bounded operators and its applications




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


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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How to Cite

G. García and G. Mora, “The degree of nondensifiability of linear bounded operators and its applications”, Appl. Gen. Topol., vol. 25, no. 1, pp. 213–228, Apr. 2024.



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