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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

No infinite dimensional $ P$ space admits a Markuschevich basis


Author: William B. Johnson
Journal: Proc. Amer. Math. Soc. 26 (1970), 467-468
MSC: Primary 46.10
MathSciNet review: 0265916
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Abstract: Theorem. Let $ X$ be a Banach space. If $ X$ is a Grothendieck space and $ X$ admits a Markuschevich basis then $ X$ is reflexive. This theorem is used to prove the conjecture of J. A. Dyer [1] stated in the title.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0265916-9
PII: S 0002-9939(1970)0265916-9
Keywords: Markuschevich basis, complete biorthogonal systems, $ P$ spaces, injective Banach spaces, Grothendieck spaces
Article copyright: © Copyright 1970 American Mathematical Society