This is an announcement for the paper "A separable L-embedded Banach space has property (X) and is therefore the unique predual of its dual" by Hermann Pfitzner.

Abstract: In this note the following is proved. Separable L-embedded spaces - that is separable Banach spaces which are complemented in their biduals such that the norm between the two complementary subspaces is additive - have property (X) which, by a result of Godefroy and Talagrand, entails uniqueness of the space as a predual.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B04, 46B03, 46B20

The source file(s), Property_X.tex: 22448 bytes, is(are) stored in gzipped form as 0507354.gz with size 8kb. The corresponding postcript file has gzipped size 41kb.

Submitted from: Hermann.Pfitzner@univ-orleans.fr

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http://front.math.ucdavis.edu/math.FA/0507354

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http://arXiv.org/abs/math.FA/0507354

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