On the Dunford-Pettis property of tensor product spaces

Ioana Ghenciu. "On the Dunford-Pettis property of tensor product spaces." Colloquium Mathematicae 125.2 (2011): 221-231. <http://eudml.org/doc/284214>.

@article{IoanaGhenciu2011,
abstract = {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.},
author = {Ioana Ghenciu},
journal = {Colloquium Mathematicae},
keywords = {Dunford-Pettis property; tensor product spaces},
language = {eng},
number = {2},
pages = {221-231},
title = {On the Dunford-Pettis property of tensor product spaces},
url = {http://eudml.org/doc/284214},
volume = {125},
year = {2011},
}

TY - JOUR
AU - Ioana Ghenciu
TI - On the Dunford-Pettis property of tensor product spaces
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 2
SP - 221
EP - 231
AB - 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.
LA - eng
KW - Dunford-Pettis property; tensor product spaces
UR - http://eudml.org/doc/284214
ER -