Common zeros preserving maps on vector-valued function spaces and Banach modules
Hosseini, Maliheh (K. N. Toosi University of Technology (Iran). Department of Mathematics)
Sady, Fereshteh (Tarbiat Modares University (Iran). Department of Pure Mathematics)

Date:	2016
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Non-vanishing functions ; Banach modules ; Maps preserving common zeros ; Vector-valued continuous function ; Point multipliers ; Zero set
Published in:	Publicacions matemàtiques, Vol. 60 Núm. 2 (2016) , p. 565-582 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/311027
DOI: 10.5565/PUBLMAT_60216_10

18 p, 379.9 KB

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