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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Lattices of uniformly continuous functions and Banach-Stone theorems
by
Jesús A. Jaramillo
Departamento de Análisis Matemático - Universidad Complutense de Madrid
Coauthors: Isabel Garrido (Universidad de Extremadura)

We are concerned here with vector lattices of uniformly continuous functions on a complete metric space X. We study real lattice homomorphisms and their representation as point evaluations. We apply our results to the lattice U(X) (respectively, L(X)) of all uniformly continuous real functions (resp. Lipschitz functions) on X, in order to obtain Banach-Stone theorems in this context. Namely, we prove that the uniform structure (resp. the Lipschitz structure) of X is characterized by the lattice U(X) (resp. L(X)).

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Date received: April 14, 2000

Copyright © 2000 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 # caey-59.