Banach-Stone theorem for Banach lattice valued continuous functions

Autor:	Z. Ercan, S. Önal
Rok vydání:	2007
Předmět:	Discrete mathematics Combinatorics Compact space Banach–Stone theorem Applied Mathematics General Mathematics Banach space Hausdorff space Isomorphism Space (mathematics) F-space Unit (ring theory) Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 135:2827-2829
ISSN:	1088-6826 0002-9939
DOI:	10.1090/s0002-9939-07-08788-6
Popis:	Let X X and Y Y be compact Hausdorff spaces, E E be a Banach lattice and F F be an AM space with unit. Let π : C ( X , E ) → C ( Y , F ) {\pi }:C(X,E)\rightarrow C(Y,F) be a Riesz isomorphism such that 0 ∉ f ( X ) 0\not \in f(X) if and only if 0 ∉ π ( f ) ( Y ) 0\not \in {\pi }(f)(Y) for each f ∈ C ( X , E ) f\in C(X,E) . We prove that X X is homeomorphic to Y Y and E E is Riesz isomorphic to F F . This generalizes some known results.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2f1149424a42ee1a37100166f347b194 https://doi.org/10.1090/s0002-9939-07-08788-6 Zobrazit plný text záznamu