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Markuschevich Bases and Duality Theory

William B. Johnson
Transactions of the American Mathematical Society
Vol. 149, No. 1 (May, 1970), pp. 171-177
DOI: 10.2307/1995669
Stable URL: http://www.jstor.org/stable/1995669
Page Count: 7
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Markuschevich Bases and Duality Theory
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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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