2018/04/29 by Ziba Pourghobadi, Pourghobadi, Z., Masoumeh Najafi Tavani +3
Mathematics · #46J10 #47B38 #47B48 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1804.10915
openalex publication_date 2018/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X and Y be compact Hausdorff spaces, E and F be real or complex Banach spaces, and A(X,E) be a subspace of C(X,E). In this paper we study linear operators S,T: A(X,E) \lo C(Y,F) which are jointly separating, in the sense that \coz(f) ∩ \coz(g) = ∅ implies that \coz(Tf) ∩ \coz(Sg)=∅. Here \coz(⋅) denotes the cozero set of a function. We characterize the general form of such maps between certain class of vector-valued (as well as scalar-valued) spaces of continuous functions including spaces of vector-valued Lipschitz functions, absolutely continuous functions and continuously differentiable functions. The results can be applied for a pair T:A(X) \lo A(X) and S:A(X,E) \lo A(X,E) of linear operators, where A(X) is a regular Banach function algebra on X, such that f⋅ g=0 implies Tf ⋅ Sg=0, for f∈ A(X) and g∈ A(X,E). If T and S are jointly separating bijections between Banach algebras of scalar-valued functions of this class, then they induce a homeomorphism between X and Y and, furthermore, T-1 and S-1 are also jointly separating maps.