Sharper bounds for the numerical radius of n�n operator matrices

Bhunia, P (2024) Sharper bounds for the numerical radius of n�n operator matrices. In: Archiv der Mathematik, 123 (2). pp. 173-183.

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Abstract

Let A=Aij be an n�n operator matrix, where each Aij is a bounded linear operator on a complex Hilbert space. Among other numerical radius bounds, we show that w(A)�w(A), where A=aij is an n�n complex matrix, with (Formula presented.) This is a considerable improvement of the existing bound w(A)�w(A~), where A~=a~ij is an n�n complex matrix, with (Formula presented.) Further, applying the bounds, we develop the numerical radius bounds for the product of two operators and the commutator of operators. Also, we develop an upper bound for the spectral radius of the sum of the product of n pairs of operators, which improves the existing bound. © Springer Nature Switzerland AG 2024.

Item Type:	Journal Article
Publication:	Archiv der Mathematik
Publisher:	Birkhauser
Additional Information:	The copyright for this article belongs to Birkhauser.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	21 Dec 2024 04:40
Last Modified:	21 Dec 2024 04:40
URI:	http://eprints.iisc.ac.in/id/eprint/85932

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