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A uniformly convex Banach space which contains no \(\ell_p\). (English) Zbl 0301.46013

MSC:
46B10 Duality and reflexivity in normed linear and Banach spaces
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46A45 Sequence spaces (including Köthe sequence spaces)
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References:
[1] W.J. Davis , T. Figiel , W.B. Johnson , and A. Pelczynski : Factoring weakly compact operators . J. Functional Anal. 17 (1974). · Zbl 0306.46020 · doi:10.1016/0022-1236(74)90044-5
[2] M.M. Day : Some more uniformly convex spaces . Bull. Amer. Math. Soc. 47 (1941) 504-507. · Zbl 0027.11003 · doi:10.1090/S0002-9904-1941-07499-9
[3] E. Dubinsky , A. Pelczynski , and H.P. Rosenthal : On Banach spaces X for which \pi 2(£\infty , X) = B(£\infty , X) . Studia Math. 44 (1972) 617-648. · Zbl 0262.46018 · eudml:217722
[4] P. Enflo : Banach spaces which can be given an equivalent uniformly convex norm . Israel J. Math. 13 (1972) 281-288. · Zbl 0259.46012 · doi:10.1007/BF02762802
[5] P. Enflo and H.P. Rosenthal : Some results concerning LP(\mu ) spaces . J. Functional Anal. 14 (1973) 325-348. · Zbl 0265.46032 · doi:10.1016/0022-1236(73)90050-5
[6] T. Figiel : An example of an infinite dimensional Banach space non-isomorphic to its Cartesian square . Studia Math. 42 (1972) 295-306. · Zbl 0213.12801 · eudml:217643
[7] R.C. James : Uniformly non-square Banach spaces . Ann. of Math. 80 (1964) 542-550. · Zbl 0132.08902 · doi:10.2307/1970663
[8] W.B. Johnson : On finite dimensional subspaces of Banach spaces with local unconditional structure . Studia Math. 51 (1974). · Zbl 0301.46012 · eudml:217915
[9] B. Maurey : Théorémes de factorisation pour les opérateurs linéaires á valeurs dans les espaces Lp . Société Mathématique de France (1974). · Zbl 0278.46028
[10] H.P. Rosenthal : On subspaces of Lp . Ann. of Math. 97 (1973) 344-373. · Zbl 0253.46049 · doi:10.2307/1970850
[11] B.S. Tsirelson : Not every Banach space contains lp or c0 .
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