Banach–Stone theorems and Riesz algebras
Copyright policy )Banach–Stone theorems and Riesz algebras
Let \(X, Y\) be compact Hausdorff spaces and let \(E, F\) be both Banach lattices and Riesz algebras. In this paper, the following main result shall be proved: If \(F\) has no zero-divisor and there exists a Riesz algebraic isomorphism \(\Phi:C(X,E)\to C(Y,F)\) such that \(\Phi(f)\) has no zero if \(f\) has none, then \(X\) is homeomorphic to \(Y\) and \(E\) is Riesz algebraically isomorphic to \(F\).
- University of Auckland New Zealand
- Tianjin University China (People's Republic of)
- Tianjin University China (People's Republic of)
- Tianjin University China (People's Republic of)
- Tianjin University China (People's Republic of)
Banach lattices, Banach–Stone theorem, Riesz algebra, Applied Mathematics, General theory of topological algebras, Banach-Stone theorem, Support, Banach lattice, Riesz algebraic isomorphism, Analysis
Banach lattices, Banach–Stone theorem, Riesz algebra, Applied Mathematics, General theory of topological algebras, Banach-Stone theorem, Support, Banach lattice, Riesz algebraic isomorphism, Analysis
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