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Title: Order isomorphisms on function spaces
Authors: Leung, D.H. 
Li, L.
Keywords: Adequate subspaces.
Phrases: order isomorphisms
Realcompact spaces
Issue Date: 2013
Citation: Leung, D.H., Li, L. (2013). Order isomorphisms on function spaces. Studia Mathematica 219 (2) : 123-138. ScholarBank@NUS Repository.
Abstract: The classical theorems of Banach and Stone (1932, 1937), Gelfand and Kolmogorov (1939) and Kaplansky (1947) show that a compact Hausdor space X is uniquely determined by the linear isometric structure, the algebraic structure, and the lattice structure, respectively, of the space C(X). In this paper, it is shown that for rather general subspaces A(X) and A(Y ) of C(X) and C(Y ), respectively, any linear bijection T : A(X) → A(Y ) such that f ≤ 0 if and only if Tf ≤ 0 gives rise to a homeomorphism h : X ! Y with which T can be represented as a weighted composition operator. The three classical results mentioned above can be derived as corollaries. Generalizations to noncompact spaces and other function spaces such as spaces of Lipschitz functions and differentiable functions are presented. © 2013 Instytut Matematyczny PAN.
Source Title: Studia Mathematica
ISSN: 00393223
DOI: 10.4064/sm219-2-3
Appears in Collections:Staff Publications

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