Bases of type and reflexivity of Banach spaces

Author:
J. R. Holub

Journal:
Proc. Amer. Math. Soc. **25** (1970), 357-362

MSC:
Primary 46.10

DOI:
https://doi.org/10.1090/S0002-9939-1970-0259567-X

MathSciNet review:
0259567

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Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to give a number of characterizations of reflexive Banach spaces having Schauder bases.

We show that a Banach space with a basis such that is contained in either or in has a basis of type . It follows that a Banach space with an unconditional basis is reflexive if and only if no basis is of type . It is also shown that a Banach space with a basis is reflexive if and only if every basis converges weakly to zero.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0259567-X

Keywords:
Schauder basis,
basic sequence,
basis of type ,
reflexive Banach space,
unconditional basis,
basis of type ,
weak convergence of bases

Article copyright:
© Copyright 1970
American Mathematical Society