Abstract
In the previous chapters the spaces ℓ p (1 ≤ p < ∞) and c 0 played a pivotal role in the development of the theory. This suggests that we should ask when we can embed one of these spaces in an arbitrary Banach space. For c 0 we have a complete answer: c 0 embeds into X if and only if X contains a WUC series that is not unconditionally convergent (Theorem 2.4.11).
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References
D.J. Aldous, Subspaces of L 1, via random measures. Trans. Am. Math. Soc. 267 (2), 445–463 (1981)
P.G. Casazza, T.J. Shura, Tsirel’son’s Space. Lecture Notes in Mathematics, vol. 1363 (Springer, Berlin, 1989). With an appendix by J. Baker O. Slotterbeck, R. Aron
P.G. Casazza, W.B. Johnson, L. Tzafriri, On Tsirelson’s space. Isr. J. Math. 47 (2–3), 81–98 (1984)
L.E. Dor, On sequences spanning a complex l 1 space. Proc. Am. Math. Soc. 47, 515–516 (1975)
T. Figiel, W.B. Johnson, A uniformly convex Banach space which contains no l p . Compos. Math. 29, 179–190 (1974)
F. Galvin, K. Prikry, Borel sets and Ramsey’s theorem. J. Symb. Logic 38, 193–198 (1973)
W.T. Gowers, B. Maurey, The unconditional basic sequence problem. J. Am. Math. Soc. 6 (4), 851–874 (1993)
R.C. James, Uniformly non-square Banach spaces. Ann. Math. (2) 80, 542–550 (1964)
R.C. James, A separable somewhat reflexive Banach space with nonseparable dual. Bull. Am. Math. Soc. 80, 738–743 (1974)
J.L. Krivine, B. Maurey, Espaces de Banach stables. Isr. J. Math. 39 (4), 273–295 (1981) (French, with English summary)
B. Maurey, Types and l 1-subspaces, in Texas Functional Analysis Seminar 1982–1983 (Texas University, Austin, 1983), pp. 123–137
V.D. Milman, Geometric theory of Banach spaces. II. Geometry of the unit ball. Usp. Mat. Nauk 26 (6), 73–149 (1971) (Russian)
E. Odell, H.P. Rosenthal, A double-dual characterization of separable Banach spaces containing l 1. Isr. J. Math. 20 (3–4), 375–384 (1975)
E. Odell, T. Schlumprecht, The distortion problem. Acta Math. 173 (2), 259–281 (1994)
F.P. Ramsey, On a problem of formal logic. Proc. Lond. Math. Soc. 30, 264–286 (1929)
H.P. Rosenthal, A characterization of Banach spaces containing l 1. Proc. Natl. Acad. Sci. U.S.A. 71, 2411–2413 (1974)
B.S. Tsirel′son, It is impossible to imbed 1 p of c 0 into an arbitrary Banach space. Funkcional. Anal. Priložen. 8 (2), 57–60 (1974) (Russian)
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Albiac, F., Kalton, N.J. (2016). ℓ p -Subspaces of Banach Spaces. In: Topics in Banach Space Theory. Graduate Texts in Mathematics, vol 233 . Springer, Cham. https://doi.org/10.1007/978-3-319-31557-7_11
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DOI: https://doi.org/10.1007/978-3-319-31557-7_11
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