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Proceedings of the American Mathematical Society

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The Phillips properties


Authors: Walden Freedman and Ali Ülger
Journal: Proc. Amer. Math. Soc. 128 (2000), 2137-2145
MSC (1991): Primary 46B20, 46B03; Secondary 46L05, 46J10
Published electronically: February 21, 2000
MathSciNet review: 1766719
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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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Additional Information

Walden Freedman
Affiliation: Department of Mathematics, College of Arts and Sciences, Koç University, 80860 Istinye, Istanbul, Turkey
Email: wfreedman@ku.edu.tr

Ali Ülger
Affiliation: Department of Mathematics, College of Arts and Sciences, Koç University, 80860 Istinye, Istanbul, Turkey
Email: aulger@ku.edu.tr

DOI: https://doi.org/10.1090/S0002-9939-00-05703-8
Keywords: Phillips lemma, Dunford-Pettis property, property $(u)$, property (V), Schur property
Received by editor(s): September 7, 1998
Published electronically: February 21, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 by Walden Freedman and Ali Ülger