Researcher: Freedman, Walden
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Freedman, Walden
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Publication Metadata only The phillips properties(American Mathematical Society (AMS), 2000) Department of Mathematics; Department of Mathematics; Department of Mathematics; Ülger, Ali; Freedman, Walden; Faculty Member; Faculty Member; College of Sciences; N/AA Banach space X has the Phillips property if the canonical projection p: X*** → X* is sequentially weak*-norm continuous, and has the weak Phillips property if p is sequentially weak*-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. © 2000 by Walden Freedman and Ali Ülger.Publication Metadata only Alternative polynomial and holomorphic Dunford-Pettis properties(Scientific and Technical research Council of Turkey - TUBITAK/Türkiye Bilimsel ve Teknik Araştırma Kurumu, 1999) Department of Mathematics; Department of Mathematics; Freedman, Walden; Faculty Member; College of Sciences; N/AAlternatives to the Polynomial Dunford-Pettis property and the Holomorphic Dunford-Pettis property, called the PDP1 and HDP1 properties, respectively, are introduced. These are shown to be equivalent to the DP1 property, an alternative Dunford-Pettis property previously introduced by the author, thus mirroring the equivalence of the three original properties. © TÜBİTAK.Publication Metadata only An extension property for banach spaces(Institute of Mathematics, Polish Academy of Sciences, 2002) Department of Mathematics; Department of Mathematics; Freedman, Walden; Faculty Member; College of Sciences; N/AA Banach space X has property (E) if every operator from X into c0 extends to an operator from X** into c0; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of being a Grothendieck space. © 2002, Instytut Matematyczny. All rights reserved.