Banach-Stone theorems and Riesz algebras |
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| Authors: | Xinhe Miao |
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| Institution: | a Department of Mathematics, Tianjin University, Tianjin 300072, PR China
b Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand |
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| Abstract: | 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  such that Φ(f) has no zero if f has none, then X is homeomorphic to Y and E is Riesz algebraically isomorphic to F. |
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| Keywords: | Banach lattice Riesz algebra Riesz algebraic isomorphism Support Banach-Stone theorem |
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