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Banach-stone theorem for Banach lattice valued continuous functions
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Date
2007-01-01
Author
Ercan, Z.
Onal, S.
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Let Chi and Upsilon be compact Hausdor spaces, Epsilon be a Banach lattice and F be an AM space with unit. Let pi : C(X, E) -> C(Upsilon, F) be a Riesz isomorphism such that 0 not subset of f (X) if and only if 0 not subset of pi (f)(Upsilon) for each f is an element of C(Chi, Epsilon). We prove that Chi is homeomorphic to Upsilon and Epsilon is Riesz isomorphic to F. This generalizes some known results.
Subject Keywords
Applied Mathematics
,
General Mathematics
URI
https://hdl.handle.net/11511/65938
Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
DOI
https://doi.org/10.1090/s0002-9939-07-08788-6
Collections
Department of Mathematics, Article
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Z. Ercan and S. Onal, “Banach-stone theorem for Banach lattice valued continuous functions,”
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
, pp. 2827–2829, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65938.