Title : ( A note on convex renorming and fragmentability )
Authors: Seyyed Alireza Kamel Mirmostafaee ,
Full TextAbstract
Abstract Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b) If the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c) If the Banach space is weakly locally uniformly rotund, then its weak topology is fragmented by a metric which is stronger than the norm topology.
Keywords
, Keywords Fragmentability of Banach spaces , topological games , renorming of Banach spaces
@article{paperid:1013770,
author = {Kamel Mirmostafaee, Seyyed Alireza},
title = {A note on convex renorming and fragmentability},
journal = {Proceedings of the Indian Academy of Sciences - Mathematical Sciences},
year = {2005},
volume = {115},
number = {2},
month = {April},
issn = {0253-4142},
pages = {201--207},
numpages = {6},
keywords = {Keywords Fragmentability of Banach spaces - topological games - renorming of Banach spaces},
}
%0 Journal Article
%T A note on convex renorming and fragmentability
%A Kamel Mirmostafaee, Seyyed Alireza
%J Proceedings of the Indian Academy of Sciences - Mathematical Sciences
%@ 0253-4142
%D 2005
