X^* with weak* uniform Kadec-Klee property has Property(K^*)

2020/05/18 by Dalby, Tim
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2005.08493

Abstract

It is shown that if the dual of a Banach space, X^*, where the dual ball is weak* sequentially compact, has the weak* uniform Kadec-Klee property then X^* has Property(K^*). An example is given where the reverse implication does not hold. That is, there is a Banach space X whose dual, X^*, has Property(K^*) but X^* does not have the weak* uniform Kadec-Klee property.

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