On nicely smooth Banach spaces
Functional Analysis
2016-09-06 v1
Abstract
In this work, we obtain some necessary and some sufficient conditions for a space to be nicely smooth, and show that they are equivalent for separable or Asplund spaces. We obtain a sufficient condition for the Ball Generated Property (BGP), and conclude that Property implies the BGP, which, in turn, implies the space is nicely smooth. We show that the class of nicely smooth spaces is stable under and sums and also under finite sums; that being nicely smooth is not a three space property; and that the Bochner spaces are nicely smooth if and only if is both nicely smooth and Asplund. A striking result obtained is that every equivalent renorming of a space is nicely smooth if and only if it is reflexive.
Keywords
Cite
@article{arxiv.math/9605213,
title = {On nicely smooth Banach spaces},
author = {Pradipta Bandyopadhyay and Sudeshna Basu},
journal= {arXiv preprint arXiv:math/9605213},
year = {2016}
}