On uniform Bishop-Phelps-Bollobás type approximations of linear operators and preservation of geometric properties

Sain, D and Mal, A and Mandal, K and Paul, K (2021) On uniform Bishop-Phelps-Bollobás type approximations of linear operators and preservation of geometric properties. In: Journal of Mathematical Analysis and Applications, 494 (1).

PDF jou_mat_ana_app_494_1.pdf - Published Version Restricted to Registered users only Download (560kB) | Request a copy

Abstract

We study uniform ϵ-BPB approximations of bounded linear operators between Banach spaces from a geometric perspective. We show that for sufficiently small positive values of ϵ, many geometric properties like smoothness, norm attainment and extremality of operators are preserved under such approximations. We present examples of pairs of Banach spaces satisfying non-trivial norm preserving uniform ϵ-BPB approximation property in the global sense. We also study these concepts in case of bounded linear operators between Hilbert spaces. Our approach in the present article leads to the improvement and generalization of some earlier results in this context. © 2020 Elsevier Inc.

Item Type:	Journal Article
Publication:	Journal of Mathematical Analysis and Applications
Publisher:	Academic Press Inc.
Additional Information:	Copyright for this article belongs to Academic Press Inc.
Keywords:	Bishop-Phelps-Bollobás property Norm attainment Extreme contractions Smooth operators
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	19 Oct 2020 11:16
Last Modified:	19 Oct 2020 11:16
URI:	http://eprints.iisc.ac.in/id/eprint/66728

Actions (login required)

View Item