Order isomorphisms on function spaces

• Autorzy: Denny H. Leung , Lei Li
• Języki publikacji: EN

Abstrakty

EN

The classical theorems of Banach and Stone (1932, 1937), Gelfand and Kolmogorov (1939) and Kaplansky (1947) show that a compact Hausdorff 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.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46E50: Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
• 47B65: Positive operators and order-bounded operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 2
• Strony: 123-138

Daty

wydano

2013

Twórcy

autor

Denny H. Leung

• Department of Mathematics, National University of Singapore, Singapore 119076

autor

Lei Li

• School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

Identyfikatory

DOI

10.4064/sm219-2-3