Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Existence of universal members in certain families of bases of Banach spaces

Author: M. Zippin
Journal: Proc. Amer. Math. Soc. 26 (1970), 294-300
MSC: Primary 46.10
MathSciNet review: 0264380
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In a recent paper A. Pełczyński proved the existence of universal Schauder bases for several important families of bases. In the present paper some new existence problems are settled. For example, it is proved that the family of boundedly complete bases does not have a universal member.

References [Enhancements On Off] (What's this?)

  • [1] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151-164. MR 22 #5872. MR 0115069 (22:5872)
  • [2] M. M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 21, Springer-Verlag, Berlin, 1958. MR 20 #1187. MR 0094675 (20:1187)
  • [3] A. Pełczyński, Universal bases, Studia Math. 32 (1969), 247-268. MR 0241954 (39:3290)
  • [4] 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 37 #3327. MR 0227743 (37:3327)
  • [5] P. Wojtaszczyk, On separable Banach spaces containing all separable reflexive Banach spaces, Studia Math. (to appear). MR 0308750 (46:7864)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.10

Retrieve articles in all journals with MSC: 46.10

Additional Information

Keywords: Universal basis, seminormalized basis, monotone basis, unconditional basis, complementably universal basis, shrinking basis, boundedly complete basis, equivalent bases, complemented subbasis, norming function, subsequence homogeneous norming function
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society