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Maps preserving common zeros between subspaces of vector-valued continuous functions. (English) Zbl 1220.47042
Suppose that X and Y are metric spaces and E and F are normed vector spaces. Denote by C(X,E) and C(Y,F) the corresponding spaces of continuous functions and by A(X,E) and A(Y,F) subspaces of C(X,E) and C(Y,F), respectively. The zero set of a function fC(X,E) is defined as Z(f)=xX:f(x)=0. The paper under review provides a complete characterization of linear and bijective maps T:A(X,E)A(Y,F) such that Z(f)Z(g) if and only if Z(fg) for any f,gA(X,E)· An application to automatic continuity is included.
MSC:
47B38Operators on function spaces (general)
46E40Spaces of vector- and operator-valued functions
46H40Automatic continuity
47B33Composition operators
References:
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