A lattice-valued Banach-Stone theorem |
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| Authors: | J Cao I Reilly H Xiong |
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| Institution: | (1) Department of Mathematics, THE University of Auckland Private Bag, 92019 Auckland, New Zealand;(2) Department of Mathematics, Tianjin Unversity, Tianjin, 30072, P. R. China |
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| Abstract: | Let X and Y be compact Hausdorff spaces, and let E be a Banach lattice. In this short note, we show that if there exists a Riesz isomorphismΦ:C(X, E) →C(Y, R) such that Φ(f) has no zeros if f has none, then X is homeomorphic to Y and E is Riesz isomorphic to R.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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| Keywords: | Riesz homomorphism Banach– Stone theorem support Banach lattice |
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