Into isometries of $C_0(X,E)$'s

Jyh-Shyang Jeang; Ngai-Ching Wong

Into isometries of $C_0(X,E)$'s

Functional Analysis 2016-09-06 v1

Authors: Jyh-Shyang Jeang , Ngai-Ching Wong

Abstract

Suppose $X$ and $Y$ are locally compact Hausdorff spaces, $E$ and $F$ are Banach spaces and $F$ is strictly convex. We show that every linear isometry $T$ from $C_0(X,E)$ {\em into} $C_0(Y,F)$ is essentially a weighted composition operator $Tf(y) = h(y) (f(\varphi(y)))$ . This supplements results of Jerison (when $T$ is onto) and Cambern (when $X,Y$ are compact).

Keywords

general topology operator theory on banach spaces banach spaces

Cite

@article{arxiv.math/9607211,
  title  = {Into isometries of $C_0(X,E)$'s},
  author = {Jyh-Shyang Jeang and Ngai-Ching Wong},
  journal= {arXiv preprint arXiv:math/9607211},
  year   = {2016}
}

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