The Phillips properties

Freedman, Walden; Ülger, Ali

doi:10.1090/S0002-9939-00-05703-8

The Phillips properties
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by Walden Freedman and Ali Ülger PDF

Proc. Amer. Math. Soc. 128 (2000), 2137-2145

Abstract:

A Banach space $X$ has the Phillips property if the canonical projection $p\colon X^{\ast \ast \ast } \rightarrow X^{\ast }$ is sequentially weak$^{\ast }$-norm continuous, and has the weak Phillips property if $p$ is sequentially weak$^{\ast }$-weak continuous. We study both properties in connection with other geometric properties, such as the Dunford-Pettis property, Pelczynski’s properties $(u)$ and (V), and the Schur property.

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