## 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

## Abstract:

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
S. Banach, - 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
S. Ulam,

*Théorie des operations linéaires*, Warsaw, 1932. J. Bourgain,

*Borel sets with*${F_{\sigma \delta }}$-

*sections*, Fund. Math. (to appear). —,

*On convergent sequences of continuous functions*, Bull. Soc. Math. Belg. (to appear). —,

*The Szlenk index and operators on*$C(K)$-

*spaces*, Bull. Soc. Math. Belg. (to appear).

*The Scottish book*, Los Alamos, 1957.

## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**79**(1980), 241-246 - MSC: Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565347-4
- MathSciNet review: 565347