Zero products preserving maps from the Fourier algebra of amenable groups

Disjointness-preserving linear maps on Banach function algebras associated with a locally compact group

“…This paper focuses on a variety of significant Banach function algebras associated with a locally compact group G such as the Figà-Talamanca-Herz algebra A p (G) and the Figà-Talamanca-Herz-Lebesgue algebra A q p (G) for p ∈ ]1, ∞[ and q ∈ [1, ∞[. Accordingly, it seems appropriate to refer the reader to the papers [1], [3]- [5], [7], [9], [12], [13], and [14]. The paper [4] is concerned with bijective disjointness-preserving linear maps Φ : A(G) → A(H) between the Fourier algebras A(G) and A(H) of amenable locally compact groups G and H. In [14], the author removes the amenability assumption and studies the continuous bijective disjointness-preserving linear maps Φ : A p (G) → A p (H) for arbitrary locally compact groups G and H. The article [12] deals with bijective disjointness-preserving linear maps between Fourier algebras, and, further, it is shown that such a map gives rise to a topological group isomorphism between the corresponding groups in the case where additionally it preserves a kind of orthogonality.…”

“…The paper [4] is concerned with bijective disjointness-preserving linear maps Φ : A(G) → A(H) between the Fourier algebras A(G) and A(H) of amenable locally compact groups G and H. In [14], the author removes the amenability assumption and studies the continuous bijective disjointness-preserving linear maps Φ : A p (G) → A p (H) for arbitrary locally compact groups G and H. The article [12] deals with bijective disjointness-preserving linear maps between Fourier algebras, and, further, it is shown that such a map gives rise to a topological group isomorphism between the corresponding groups in the case where additionally it preserves a kind of orthogonality. In [3] and [13], the operator space structure of the Fourier algebra A(G) of a locally compact group G is involved, and the authors are concerned with completely bounded surjective disjointness-preserving linear maps from A(G) in the case where G is amenable. Further, articles [1] and [5] are devoted to group algebras ( [5] is restricted to locally compact abelian groups).…”