Norm inequalities in L(X) and a geometric constant

Bhunia, P and Mal, A (2024) Norm inequalities in L(X) and a geometric constant. In: Banach Journal of Mathematical Analysis, 18 (2).

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Abstract

We introduce a new norm (say α-norm) on L(X), the space of all bounded linear operators defined on a normed linear space X. We explore various properties of the α-norm. In addition, we study several equalities and inequalities of the α-norm of operators on X. As an application, we obtain an upper bound for the numerical radius of product of operators, which improves a well-known upper bound of the numerical radius for sectorial matrices. We present the α-norm of operators by using the extreme points of the unit ball of the corresponding spaces. Furthermore, we define a geometric constant (say α-index) associated with X and study properties of the α-index. In particular, we obtain the exact value of the α-index for some polyhedral spaces and complex Hilbert space. Finally, we study the α-index of �p-sum of normed linear spaces. © Tusi Mathematical Research Group (TMRG) 2024.

Item Type:	Journal Article
Publication:	Banach Journal of Mathematical Analysis
Publisher:	Birkhauser
Additional Information:	The copyright for this article belongs to Birkhauser.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	11 Jul 2024 05:24
Last Modified:	11 Jul 2024 05:24
URI:	http://eprints.iisc.ac.in/id/eprint/84800

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