Representation theorems for Banach algebras

For a space X denote by C-b(X) the Banach algebra of all continuous bounded scalar-valued functions on X and denote by C-0(X) the set of all elements in C-b(X) which vanish at infinity. We prove that certain Banach subalgebras H of C-b(X) are isometrically isomorphic to C-0(Y), for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y is explicitly constructed as a subspace of the Stone-Cech compactification of X. The known construction of Y enables us to examine certain properties of either H or Y and derive results not expected to be deducible from the standard Gelfand Theory. (C) 2013 Elsevier B.V. All rights reserved.