On the convergence of some spectral characteristics of the converging operator sequences

Bhunia, P and Ipek Al, P and Ismailov, ZI (2024) On the convergence of some spectral characteristics of the converging operator sequences. In: Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 134 (1).

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Abstract

Convergence of the differences between operator norm and spectral radius, operator norm and numerical radius, numerical radius and spectral radius, operator norm and Crawford number, operator norm and subspectral radius of complex Hilbert space operator sequences (which are uniformly convergent) has been investigated. Also, an inequality for the difference of Crawford numbers of two linear bounded operators A and B has been obtained. It is shown that (Formula presented.) where c(·) and �(·) denote the Crawford number and the numerical radius, respectively. The results have been supported by an example. Finally, some applications to operator Hölder functions and operator-functions have been given. © Indian Academy of Sciences 2024.

Item Type:	Journal Article
Publication:	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Publisher:	Springer
Additional Information:	The copyright for this article belongs to the Springer.
Keywords:	47a05; 47a10; 47a12; 47a30; Crawford number; Numerical radius; Operator norm; Spectral characteristics; Spectral radius; Uniformly convergence, Matrix algebra
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	24 Apr 2024 05:39
Last Modified:	24 Apr 2024 05:39
URI:	https://eprints.iisc.ac.in/id/eprint/84607

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