• Very smooth points of spaces of operators

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/113/01/0053-0064

• # Keywords

Very smooth points; spaces of operators; M-ideals

• # Abstract

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is anM-ideal in the space of bounded operators, a very smooth operatorT attains its norm at a unique vectorx (up to a constant multiple) andT(x) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon-Nikodým property. We give an example of a smooth Banach space without any very smooth points.

• # Author Affiliations

1. Indian Statistical Institute, R.V. College Post, Bangalore - 560 059, India

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019