Orthogonality and disjointness preserving linear maps between Fourier and Fourier–Stieltjes algebras of locally compact groups

Abstract

This paper is devoted to the study of orthogonality and disjointness preserving linear maps between Fourier and Fourier-Stieltjes algebras of locally compact groups. We show that a linear bijection Ψ :) between two Fourier algebras (resp. Fourier-Stieltjes algebras) of locally compact groups will induce a topological group isomorphism between G 1 and G 2 , provided that Ψ preserves both disjointness and some kind of orthogonality. This improves earlier results of J. J. Font and M. S. Monfared, where amenability of the groups or continuity of the linear maps are assumed. We also study the structure of bounded and unbounded disjointness preserving linear functionals of Fourier algebras. In the development, general results about disjointness and orthogonality preserving linear maps between C*-algebras, W*-algebras and their preduals are obtained.

Arens regularity of ideals of the group algebra of a compact Abelian group

“…Let U ⊆ K be a neighbourhood of p with α(x 0 ) / ∈ U . By Lemma 3.1 of [38], there are, for each n ∈ N, a neighbourhood V n of p and u n ∈ A(K) such that…”

Complete orthogonality preservers between C⁎-algebras

“…We show a similar useful characterisation for right orthogonality. Right (left) orthogonality preserving operators have also been studied in the contexts of C * -algebras and preduals of von Neumann algebras (see [23]). The reader can check the survey [24] and references therein for the main results on zeroproduct, orthogonality or right (left) orthogonality preserving operators between C * -algebras and some other related structures.…”

Weight-preserving isomorphisms between spaces of continuous functions: The scalar case

“…Separating isomorphisms have been studied by many workers and have found application to a variety of fields (cf. [1,2,3,4,7,8,9,14,15,17,19,20,21]). After Corollary 3.3, it is clear that, in order to prove Theorem 1.6, it suffices to deal with the broader case of separating isomorphisms and so we do in the rest of the paper.…”