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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Banach spaces with separable duals

Author: M. Zippin
Journal: Trans. Amer. Math. Soc. 310 (1988), 371-379
MSC: Primary 46B15; Secondary 46B10
MathSciNet review: 965758
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Abstract: It is proved that every Banach space with a separable dual embeds into a space with a shrinking basis. It follows that every separable reflexive space can be embedded in a reflexive space with a basis.

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  • [1] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327. MR 0355536 (50:8010)
  • [2] D. W. Dean, J. Singer and L. Sternbach, On shrinking basis sequences in Banach spaces, Studia Math. 40 (1971), 23-33. MR 0306876 (46:5998)
  • [3] W. B. Johnson and H. P. Rosenthal, On $ {\omega ^{\ast}}$-basic sequences and their applications to the study of Banach spaces, Studia Math. 43 (1972), 77-92. MR 0310598 (46:9696)
  • [4] W. B. Johnson, H. P. Rosenthal and M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488-506. MR 0280983 (43:6702)
  • [5] R. Haydon, An extreme point criterion for separability of a dual Banach space and a new proof of a theorem of Corson, Quart. J. Math. Oxford 27 (1976), 378-385. MR 0493264 (58:12293)
  • [6] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Vol. I, Springer-Verlag, Berlin, Heidelberg and New York, 1977. MR 0415253 (54:3344)
  • [7] A. Pełczyński, Some problems on bases in Banach and Frechet spaces, Israel J. Math. 2 (1964), 132-138. MR 0173141 (30:3356)
  • [8] -, Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239-242. MR 0308753 (46:7867)
  • [9] M. Zippin, The separable extension problem, Israel J. Math. 26 (1977), 372-387. MR 0442649 (56:1030)

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Article copyright: © Copyright 1988 American Mathematical Society

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