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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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Stability of Disjointness Preserving Mappings
by
Gregor Dolinar
University of Ljubljana

Let X and Y be compact Hausdorff spaces and let \epsilon >= 0. A linear mapping \Phi: C(X) --> C(Y) is called \epsilon-disjointness preserving if f g = 0 implies that ||\Phi(f) \Phi(g)|| <= \epsilon||f|| ||g||. If \Phi:C(X) --> C(Y) is a continuous or surjective \epsilon-disjointness preserving linear mapping, we prove that there exists a disjointness preserving linear mapping \Psi: C(X) --> C(Y) satisfying || \Phi(f) - \Psi(f)|| <= 20\epsilon1/2 ||f||. We also prove that every unbounded \epsilon-disjointness preserving linear functional on C(X) is disjointness preserving.

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Date received: January 24, 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 # caei-03.