Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.

The structure of compact disjointness preserving operators on continuous functions

Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Snd ?hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator