Maps preserving common zeros between subspaces of vector-valued continuous functions |
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Authors: | Luis Dubarbie |
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Institution: | 1.Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias,Universidad de Cantabria,Santander,Spain |
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Abstract: | For metric spaces X and Y, normed spaces E and F, and certain subspaces A( X, E) and A( Y, F) of vector-valued continuous functions, we obtain a complete characterization of linear and bijective maps \({T:A(X,E)\rightarrow A(Y,F)}\) preserving common zeros, that is, maps satisfying the property $Z(f) \cap Z(g) \neq \emptyset \Longleftrightarrow Z(Tf) \cap Z(Tg) \neq \emptyset \quad\quad\quad{\rm (P)}$ for any \({f, g \in A(X, E)}\), where \({Z(f) = \{x \in X: f(x) = 0\}}\). Moreover, we provide some examples of subspaces for which the automatic continuity of linear bijections having the property (P) is derived. |
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