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.)