Abstract
We construct a Banach spaceE, which has the Banach-Saks property and such thatL 2(E) does not have the Banach-Skas property. The construction is a somewhat tree-like modification of Baernstein’s space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Baernstein,On reflexivity and summability, Studia Math.42 (1972), 91–94.
B. Beauzamy,Banach Saks properties and spreading models, Math. Scand.44 (1979), 357–384.
J. Bourgain,On the Banach-Saks property in Lebesgue spaces, Vrije Universiteit Brussel, preprint, 1979.
W. J. Davis, T. Figiel, W. B. Johnson and A. Pelczynski,Factoring weakly compact operators, J. Functional Analysis17 (1974), 311–327.
J. Diestel and J. J. Uhl, Jr.,Vector Measures, Surveys of the Amer. Math. Soc. 15, Rhode Island, 1977.
S. Guerre,La propriété de Banach-Saks ne passe pas de E à L 2(E), d’après J. Bourgain, Séminaire d’Analyse Fonctionelle, Ecole Polytechnique Paris, 1979/80.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schachermayer, W. The Banach-Saks property is notL 2-hereditary. Israel J. Math. 40, 340–344 (1981). https://doi.org/10.1007/BF02761374
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02761374