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Some isomorphic properties in $K(X,Y)$ and in projective tensor products

Volume 146 / 2017

Raffaella Cilia, Giovanni Emmanuele Colloquium Mathematicum 146 (2017), 239-252 MSC: Primary 46B20, 46B28, 46M05. DOI: 10.4064/cm6184-12-2015 Published online: 7 October 2016

Abstract

We study the (DPrcp) property and the Gelfand–Phillips properties in spaces of compact operators. Moreover we give some sufficient conditions implying that the projective tensor product of two Banach spaces is sequentially right (SR) or has the L-limited property. We introduce the dual (SR$^*$) property and we give a characterization of it, also showing that it is intermediate between the (V$^*)$ and the (RDP$^*)$ properties. Finally, we study the Bourgain–Diestel property (BD) and the (RDP$^*)$ property in the space $K_{w^*\hbox {-}w}(X^*,Y).$

Authors

  • Raffaella CiliaDipartimento di Matematica ed Informatica
    Università di Catania
    Viale Andrea Doria 6
    95125 Catania, Italy
    e-mail
  • Giovanni EmmanueleDipartimento di Matematica ed Informatica
    Università di Catania
    Viale Andrea Doria 6
    95125 Catania, Italy
    e-mail

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