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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On the existence of strongly series summable Markuschevich bases in Banach spaces


Author: William B. Johnson
Journal: Trans. Amer. Math. Soc. 157 (1971), 481-486
MSC: Primary 46.10
MathSciNet review: 0282201
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Abstract: The main result is: Let $ X$ be a complex separable Banach space. If the identity operator on $ {X^ \ast }$ is the limit in the strong operator topology of a uniformly bounded net of linear operators of finite rank, then $ X$ admits a strongly series summable Markuschevich basis.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0282201-5
PII: S 0002-9947(1971)0282201-5
Keywords: Strongly series summable Markuschevich bases, complete biorthogonal sequences, Schauder bases, metric approximation property
Article copyright: © Copyright 1971 American Mathematical Society