Common zeros preserving maps on vector-valued function spaces and Banach modules
Let X, Y be Hausdorff topological spaces, and let E and F be Hausdorff topological vector spaces. For certain subspaces A (X,E) and A(Y, F) of C(X,E) and C(Y, F) respectively (including the spaces of Lipschitz functions), we characterize surjections S, T : A (X;E) → A(Y, F), not assumed to be linear...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:160583 |
| Acceso en línea: | https://ddd.uab.cat/record/160583 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_60216_10 |
| Access Level: | acceso abierto |
| Palabra clave: | Non-vanishing functions Banach modules Maps preserving common zeros Vector-valued continuous function Point multipliers Zero set |
| Sumario: | Let X, Y be Hausdorff topological spaces, and let E and F be Hausdorff topological vector spaces. For certain subspaces A (X,E) and A(Y, F) of C(X,E) and C(Y, F) respectively (including the spaces of Lipschitz functions), we characterize surjections S, T : A (X;E) → A(Y, F), not assumed to be linear, which jointly preserve common zeros in the sense that Z (f - f') ∩ Z (f - f') ∩ Z (g - g') ≠ 0 if and only if Z (Sf - Sf') ∩ Z (Tg - Tg') ≠ 0 for all f, f', g, g' ∈ A (X, E). Here Z (·)denotes the zero set of a function. Using the notion of point multipliers we extend the notion of zero set for the elements of a Banach module and give a representation for surjective linear maps which jointly preserve common zeros in module case. |
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