Extreme points of the unit ball of L(X)w⁎ and best approximation in L(X)w

Mal, A (2022) Extreme points of the unit ball of L(X)w⁎ and best approximation in L(X)w. In: Bulletin des Sciences Mathematiques, 179 .

PDF bul_des_sci_mat_179_2022.pdf - Published Version Restricted to Registered users only Download (342kB) | Request a copy

Abstract

We study the geometry of L(X)w, the space of all bounded linear operators on a Banach space X, endowed with the numerical radius norm, whenever the numerical radius defines a norm. We obtain the form of the extreme points of the unit ball of the dual space of L(X)w. Using this structure, we explore Birkhoff-James orthogonality, best approximation and deduce distance formula in L(X)w. A special attention is given to the case of operators satisfying a notion of smoothness. Finally, we obtain an equivalence between Birkhoff-James orthogonality in L(X)w and that in X.

Item Type:	Journal Article
Publication:	Bulletin des Sciences Mathematiques
Publisher:	Elsevier Masson s.r.l.
Additional Information:	The copyright for this article belongs to the Elsevier Masson s.r.l.
Keywords:	Best approximation; Birkhoff-James orthogonality; Distance formula; Linear operators; Numerical radius
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	10 Aug 2022 05:34
Last Modified:	10 Aug 2022 05:34
URI:	https://eprints.iisc.ac.in/id/eprint/75768

Actions (login required)

View Item