Common zeros preserving maps on vector-valued function spaces and Banach modules

• Autores: Malileh Hosseini, Fereshteh Sady
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 60, Nº 2, 2016, págs. 565-582
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.