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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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Moment problems for commuting pairs of contractions
by
Doru Paunescu
Polytechnical Institute, Timisoara
Coauthors: Pasc Gavruta

Let H be a complex Hilbert space and L( H) the C * -algebra of all bounded linear operators on H; an element of ( L( H) ) 1- , the (closed) unit ball of L( H) , will be called contraction on H.

In 1982 Zoltán Sebestyén (see [2]) solved the following moment problem:

Given a sequence { hn} n in N of elements of the Hilbert space H under what condition does there exist a contraction T on H  such that
hn=Tnh0      \textholds for  n=1, 2, ...     ? \tag\QTRit1
(\theequation)
The key to the solutions is the theory of unitary dilations. His answer is the following:

Theorem. Let { hm} m in N be a sequence of elements of the Hilbert space H. There exists a contraction satisfying ( 1) if and only if

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-52.