Real-Multilinear Isometries on Function Algebras

Abstract

Let A 1 ,...,A k be function algebras (or more generally, dense subspaces of uniformly closed function algebras) on locally compact Haus- dorff spaces X 1 ,...,X k , respectively, and let Y be a locally compact Hausdorff space. A k -real-linear map T : A 1 × ··· × A k −→ C 0 ( Y )is called a real-multilinear (or k -real-linear) isometry if

T ( f 1 ,...,f k )

= k

i =1

f i

(( f 1 ,...,f k ) ∈ A 1 ×···× A k ) , where · denotes the supremum norm. In this paper we study such maps and obtain generalizations of basically all known results concerning multilinear and real-linear isometries on function algebras.