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Uniqueness of preduals in spaces of operators

Published:2014-02-01

• G. Godefroy,
Institut de Mathématiques de Jussieu, 4 place Jussieu, 75005 Paris, France
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Abstract

We show that if $E$ is a separable reflexive space, and $L$ is a weak-star closed linear subspace of $L(E)$ such that $L\cap K(E)$ is weak-star dense in $L$, then $L$ has a unique isometric predual. The proof relies on basic topological arguments.
 MSC Classifications: 46B20 - Geometry and structure of normed linear spaces 46B04 - Isometric theory of Banach spaces