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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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On some vector-valued Banach-Stone theorems
by
Jiling Cao
Ehime University, Japan

The well-known Banach-Stone theorem says: For any two compact Hausdorff spaces X and Y, C(X) being linearly isometric to C(Y) as Banach spaces implies that X and Y are homeomorphic. In this talk, we shall discuss some possible extensions of this theorem to vector-valued function spaces. In particular, the following result shall be presented.

Theorem. Let X and Y be compact Hausdorff spaces, let E and F be Banach lattices satisfying the following property: /\ j=1n xj > \theta whenever xj > \theta for all 1 <= j <= n, and any n in N. If there is a Riesz isomorphism \Psi: C(X, E) --> C(Y, F) such that \Phi(f) is non-vanishing if f is non-vanishing, then X and Y are homeomorphic, E and F are Riesz isomorphic.

Date received: June 13, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-42.