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Transactions of the American Mathematical Society

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Markuschevich bases and duality theory


Author: William B. Johnson
Journal: Trans. Amer. Math. Soc. 149 (1970), 171-177
MSC: Primary 46.01
DOI: https://doi.org/10.1090/S0002-9947-1970-0261312-3
MathSciNet review: 0261312
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Abstract: Several duality theorems concerning Schauder bases in locally convex spaces have analogues in the theory of Markuschevich bases. For example, a locally convex space with a Markuschevich basis is semireflexive iff the basis is shrinking and boundedly complete.

The strong existence Theorem III.1 for Markuschevich bases allows us to show that a separable Banach space is isomorphic to a conjugate space iff it admits a boundedly complete Markuschevich basis, and that a separable Banach space has the metric approximation property iff it admits a Markuschevich basis which is a generalized summation basis in the sense of Kadec.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0261312-3
Keywords: Schauder basis, biorthogonal system, metric approximation property, semireflexivity
Article copyright: © Copyright 1970 American Mathematical Society

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