On separable Banach spaces, universal for all separable reflexive spaces

On separable Banach spaces, universal for all separable reflexive spaces
HTML articles powered by AMS MathViewer

by J. Bourgain PDF

Proc. Amer. Math. Soc. 79 (1980), 241-246 Request permission

It is shown that a separable Banach space which is universal for all separable reflexive spaces is also universal for all separable spaces.

References

Dale E. Alspach, Quotients of $C[0,\,1]$ with separable dual, Israel J. Math. 29 (1978), no. 4, 361–384. MR 491925, DOI 10.1007/BF02761174

Théorie des operations linéaires

Borel sets with

sections

On convergent sequences of continuous functions

The Szlenk index and operators on

spaces

C. Dellacherie, Les dérivations en théorie descriptive des ensembles et le théorème de la borne, Séminaire de Probabilités, XI (Univ. Strasbourg, Strasbourg, 1975/1976) Lecture Notes in Math., Vol. 581, Springer, Berlin, 1977, pp. 34–46 (French). MR 0454942
Per Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13 (1972), 281–288 (1973). MR 336297, DOI 10.1007/BF02762802
D. P. Giesy and R. C. James, Uniformly non-$l^{(1)}$ and $B$-convex Banach spaces, Studia Math. 48 (1973), 61–69. MR 333669, DOI 10.4064/sm-48-1-61-69
James Hagler, A counterexample to several questions about Banach spaces, Studia Math. 60 (1977), no. 3, 289–308. MR 442651, DOI 10.4064/sm-60-3-289-308
Robert C. James, A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc. 80 (1974), 738–743. MR 417763, DOI 10.1090/S0002-9904-1974-13580-9
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
W. Szlenk, The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces, Studia Math. 30 (1968), 53–61. MR 227743, DOI 10.4064/sm-30-1-53-61

The Scottish book