Characterization of extreme contractions through $k-$smoothness of operators

TL;DR

This paper characterizes extreme contractions between finite-dimensional polyhedral Banach spaces using $k$-smoothness, explores the weak L-P property, and computes the number of extreme contractions in specific spaces, advancing understanding in this area.

Contribution

It introduces new characterizations of extreme contractions via $k$-smoothness and provides conditions for the weak L-P property, generalizing previous results.

Findings

Characterization of extreme contractions using $k$-smoothness.

A sufficient condition for the weak L-P property.

Explicit computation of extreme contractions in certain Banach spaces.

Abstract

We characrterize extreme contractions defined between \ finite-dimensional polyhedral Banach spaces using $k$- smoothness of operators. We also explore weak L-P property, a recently introduced concept in the study of extreme contractions. We obtain a sufficient condition for a pair of finite-dimensional polyhedral Banach spaces to satisfy weak L-P property. As an application of these results, we explicitly compute the number of extreme contractions in some special Banach spaces. Our approach in this paper in studying extreme contractions lead to the improvement and generalization of previously known results.