On the Dunford-Pettis property of tensor product spaces

• Autorzy: Ioana Ghenciu
• Języki publikacji: EN

Abstrakty

EN

We give sufficient conditions on Banach spaces E and F so that their projective tensor product $E ⊗ _π F$ and the duals of their projective and injective tensor products do not have the Dunford-Pettis property. We prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T:E* → F** is completely continuous, then $(E ⊗ _ϵ F)*$ does not have the DPP. We also prove that if E* does not have the Schur property, F is infinite-dimensional, and every operator T: F** → E* is completely continuous, then $(E ⊗ _πF)* ≃ L(E,F*)$ does not have the DPP.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B25: Classical Banach spaces in the general theory
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 2
• Strony: 221-231

Daty

wydano

2011

Twórcy

autor

Ioana Ghenciu

• Mathematics Department, University of Wisconsin-River Falls, River Falls, WI 54022, U.S.A.

Identyfikatory

DOI

10.4064/cm125-2-7