Schatten p-Norm and Numerical Radius Inequalities with Applications

Bhunia, P and Sahoo, S (2025) Schatten p-Norm and Numerical Radius Inequalities with Applications. In: Results in Mathematics, 80 (1).

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Abstract

We develop a new refinement of the Kato�s inequality and using this refinement we obtain several upper bounds for the numerical radius of a bounded linear operator as well as the product of operators, which improve the well known existing bounds. Further, we obtain a necessary and sufficient condition for the positivity of 2�2 certain block matrices and using this condition we deduce an upper bound for the numerical radius involving a contraction operator. Furthermore, we study the Schatten p-norm inequalities for the sum of two n�n complex matrices via singular values, and from the inequalities we obtain the p-numerical radius and the classical numerical radius bounds. We show that for every p>0, the p-numerical radius wp(·):Mn(C)�R satisfies wp(T)�12|T|2(1-t)+|T�|2(1-t)�|T|2t+|T�|2t�p/2 for all t�0,1. Considering p��, we get a nice refinement of the well known classical numerical radius bound w(T)�12T�T+TT�. As an application of the Schatten p-norm inequalities we develop a bound for the energy of a graph. We show that E(G)�2mmax1�i�n�j,vi�vjdj, where E(G) is the energy of a simple graph G with m edges and n vertices v1,v2,�,vn such that degree of vi is di for each i=1,2,�,n. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

Item Type:	Journal Article
Publication:	Results in Mathematics
Publisher:	Birkhauser
Additional Information:	The copyright for this article belongs to publishers.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Dec 2024 05:04
Last Modified:	30 Dec 2024 05:04
URI:	http://eprints.iisc.ac.in/id/eprint/87168

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