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Some strongly bounded classes of Banach spaces. (English) Zbl 1115.03061
Summary: We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht [Math. Ann. 335, 901–916 (2006; Zbl 1108.46007)], asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach space.

MSC:
03E15 Descriptive set theory
46B03 Isomorphic theory (including renorming) of Banach spaces
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