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18th International Conference on Operator Theory
June 27 - July 1, 2000
University of the West
Timisoara, Romania

Organizers
Dumitru Gaspar, Traian Ceausu, Aurelian Craciunescu, Aurelian Gheondea, Radu-Nicolae Gologan, Ciprian Pop, Dan Popovici, Nicolae Suciu, Alexandru Terescenco, Dan Timotin, Flavius Turcu

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Fuglede-type property of operator representations
by
Marek Kosiek
Instytut Matematyki, Uniwersytet Jagiellonski, Kraków, Poland

We consider contractive operator representations \Phi: A --> L(H) for a given function algebra A on a compact set X and a given Hilbert space H. If we take its Lebesgue-type decomposition with respect to a reducing band B subset C(X)* i.e. the decomposition
\Phi = \Phi1\oplus\Phi2,
where \Phi1 : A --> L(H1) is a representation absolutely continuous with respect to B, \Phi2 : A --> L(H2) is singular to B and H=H1\oplusH2, then it appears that the subspaces H1, H2 are not only reducing for \Phi but also for its commutant. As an example of the application we get Lebesgue-type decompositions for n-tuples of commuting Hilbert space contractions without assuming for them any kind of von Neumann inequality.

Date received: June 5, 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 # caeo-50.