Abstract. We give a description of all 2-local (surjective linear) isometries of $C_0(X)$ where $X$ is a locally compact Hausdorff space. Further, we prove that if $X$ is also first countable and $\sigma $-compact then every 2-local (surjective linear) isometry of $C_0(X)$ is a (surjective linear) isometry. Finally, we show that this result cannot be generalized for arbitrary locally compact Hausdorff spaces.
AMS Subject Classification
(1991): 46J10, 47B38
Keyword(s):
Reflexivity,
isometry,
local isometry,
2-local isometry,
function algebra
Received May 21, 2001. (Registered under 2814/2009.)
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