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Proceedings of the American Mathematical Society
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
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0264380-3
PII: S 0002-9939(1970)0264380-3
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