Disjointness preserving mappings between Fourier algebras

Disjointness preserving mappings on BSE Ditkin algebras

“…[1], [2] or [6]), on spaces of continuous functions (see e.g. [14], [3], [7], [15] or [12]), on group algebras of locally compact Abelian groups ( [8]), on Fourier algebras ( [10] and [20]) and on some others (see e.g. [16], [17] or [5]).…”

Completely bounded disjointness preserving operators between Fourier algebras

“…It is clear that a homomorphism preserves disjointness of cozero sets of functions, hence is a disjointness preserving operator. In [6,7], Font studied bounded disjointness preserving bijections between Fourier algebras, and showed that such an operator is a weighted composition operator. In a recent paper [1], the authors introduced the concept of property (A) and studied such maps in the setting of Banach algebras with property (A).…”

“…In this paper, we completely characterize such operators in the case the involved groups are amenable. Our characterization takes into account the algebraic structure of the underlying groups, and not only their topology, which was the primary emphasis in [6,7].…”

Characterizations of Disjointness preserving operators on vector-valued function spaces

“…Lately such operators were studied between the spaces of real or complex-valued continuous functions under the name of separating operators (see, e.g., [8,5]), or between Fourier algebras (e.g. [6]). It was shown that a bounded disjointness preserving operator is a weighted composition operator.…”