Local isometries on subspaces and subalgebras of function spaces

Abstract

. Let K denotes the field of real or complex numbers. For a locally compact Hausdorff space X , we denote by C 0 ( X ) the space of all K -valued continuous functions on X vanishing at infinity. Let E be a (real or complex) Banach space, K E be a closed subset of E , and C u ( K E ) be the algebra of all real or complex valued, uniformly continuous bounded functions defined on K E . Endowed with the supremum norm, both C 0 ( X ) and C u ( K E ) are Banach spaces. In this paper we study the structure of local isometries on subspaces of C 0 ( X ) and various subalgebras of C u ( K E ) .