Local isometries of ℒ(𝒳,𝒞(𝒦))

Rao, T.

doi:10.1090/S0002-9939-05-07832-9

Local isometries of $\mathcal {L}(X,C(K))$
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by T. S. S. R. K. Rao PDF

Proc. Amer. Math. Soc. 133 (2005), 2729-2732 Request permission

Abstract:

In this paper we study the structure of local isometries on $\mathcal {L}(X,C(K))$. We show that when $K$ is first countable and $X$ is uniformly convex and the group of isometries of $X^\ast$ is algebraically reflexive, the range of a local isometry contains all compact operators. When $X$ is also uniformly smooth and the group of isometries of $X^\ast$ is algebraically reflexive, we show that a local isometry whose adjoint preserves extreme points is a $C(K)$-module map.

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