Quasi-Reflexivity and Weakly UnconditionallyConvergeant Series
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J.R. RETHERFORD (1967)
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Andrew John Sommese (1976)
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G. Sirvint (1950)
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S. SIMONS (1968)
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W. HUNSAKER, W. LINDGREN (1970)
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D.A. MATTSON (1967)
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J. H. Qiu (2004)
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Every weakly countably compact closed convex set in a locally convex space has the quasi-weak drop property.
Gilles Godefroy (1981)
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I.L. REILLY (1970)
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D. van Dulst (1976)
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Baker, C.W. (2002)
International Journal of Mathematics and Mathematical Sciences
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G. Schlüchtermann (1992)
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A new drop property, the quasi-weak drop property, is introduced. Using streaming sequences introduced by Rolewicz, a characterisation of the quasi-weak drop property is given for closed bounded convex sets in a Fréchet space. From this, it is shown that the quasi-weak drop property is equivalent to weak compactness. Thus a Fréchet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.