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Separable L‐embedded Banach spaces are unique preduals
Author(s) -
Pfitzner Hermann
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm077
Subject(s) - mathematics , separable space , banach space , linear subspace , uniqueness , norm (philosophy) , lp space , pure mathematics , eberlein–šmulian theorem , interpolation space , banach manifold , discrete mathematics , functional analysis , mathematical analysis , biochemistry , chemistry , political science , law , gene
In this note the following is proved. Separable L‐embedded spaces – that is separable Banach spaces which are complemented in their biduals and 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.