Additive jointly separating maps and ring homomorphisms

2019/07/24 by Sady, Fereshteh, Tavani, Masoumeh Najafi
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1907.10286

Abstract

Let X and Y be compact Hausdorff spaces, E and F be real or complex normed spaces and A(X,E) be a subspace of C(X,E). For a function f∈ C(X,E), let \coz(f) be the cozero set of f. A pair of additive maps S,T: A(X,E) \lo C(Y,F) is said to be jointly separating if \coz(Tf)∩ \coz(Sg)=∅ whenever \coz(f)∩ \coz(g)= ∅. In this paper, first we give a partial description of additive jointly separating maps between certain spaces of vector-valued continuous functions (including spaces of vector-valued Lipschitz functions, absolutely continuous functions and continuously differentiable functions). Then we apply the results to characterize continuous ring homomorphisms between certain Banach algebras of vector-valued continuous functions. In particular, the results provide some generalizations of the recent results on unital homomorphisms between vector-valued Lipschitz algebras, with a different approach.

Related

• Jointly separating maps between vector-valued function spaces
• Compact homomorphisms between algebras of C(K)-valued Lipschitz functions
• Separating maps between commutative Banach algebras
• On extendibility and decomposability of certain *-linear maps into C (X)
• Banach-Stone Theorems for maps preserving common zeros