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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0264380-3
MathSciNet review:
0264380
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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.
- C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI https://doi.org/10.4064/sm-17-2-151-164
- Mahlon M. Day, Normed linear spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 21, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. Reihe: Reelle Funktionen. MR 0094675
- A. Pełczyński, Universal bases, Studia Math. 32 (1969), 247–268. MR 241954, DOI https://doi.org/10.4064/sm-32-3-247-268
- 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 https://doi.org/10.4064/sm-30-1-53-61
- Przemysław Wojtaszczyk, On separable Banach spaces containing all separable reflexive Banach spaces, Studia Math. 37 (1970/71), 197–202. MR 308750, DOI https://doi.org/10.4064/sm-37-2-197-202
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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