Estimates of Euclidean numerical radius for block matrices

Bhunia, P and Jana, S and Paul, K (2024) Estimates of Euclidean numerical radius for block matrices. In: Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 134 (2).

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Abstract

We develop several Euclidean numerical radius bounds for the product of two d-tuple operators using positivity criteria of a 2�2 block matrix whose entries are d-tuple operators. From these bounds, by using polar decomposition of operators, we obtain Euclidean numerical radius bounds for d-tuple operators. Among many other bounds, it is shown that (Formula presented.) where we(A) and �A� are the Euclidean numerical radius and the Euclidean operator norm, respectively, of a d-tuple operator A=(A1,A2,�,Ad). Further, we develop an upper bound for the Euclidean numerical radius of an n�n operator matrix whose entries are d-tuple operators. In particular, it is proved that if Aijn�n is an n�n operator matrix then (Formula presented.) where each Aij is a d-tuple operator, 1�i,j�n, aij=we(Aij) if i=j, aij=we(|Aji|+|Aij�|)we(|Aij|+|Aji�|) if i<j, and aij=0 if i>j. Some related applications are also discussed. © 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 Springer.
Keywords:	47a30; 47a50; Euclidean; Euclidean numerical radius; Euclidean operator norm; Inequality; Numerical radius; Operator norm; Primary: 47a12; Secondary: 15a60, Matrix algebra
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	16 Dec 2024 10:18
Last Modified:	16 Dec 2024 10:18
URI:	http://eprints.iisc.ac.in/id/eprint/85789

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