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The Banach-Saks property is not \(L^ 2-\)hereditary. (English) Zbl 0486.46021

MSC:
46B20 Geometry and structure of normed linear spaces
46B25 Classical Banach spaces in the general theory
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E40 Spaces of vector- and operator-valued functions
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References:
[1] A. Baernstein,On reflexivity and summability, Studia Math.42 (1972), 91–94.
[2] B. Beauzamy,Banach Saks properties and spreading models, Math. Scand.44 (1979), 357–384. · Zbl 0427.46007
[3] J. Bourgain,On the Banach-Saks property in Lebesgue spaces, Vrije Universiteit Brussel, preprint, 1979. · Zbl 0434.46016
[4] W. J. Davis, T. Figiel, W. B. Johnson and A. Pelczynski,Factoring weakly compact operators, J. Functional Analysis17 (1974), 311–327. · Zbl 0306.46020 · doi:10.1016/0022-1236(74)90044-5
[5] J. Diestel and J. J. Uhl, Jr.,Vector Measures, Surveys of the Amer. Math. Soc. 15, Rhode Island, 1977.
[6] 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.
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