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UNITARY PROPAGATION OF OPERATOR DATA

Published online by Cambridge University Press:  08 January 2008

Zenon J. JabŁoński ,
Jan Stochel  and
Franciszek Hugon Szafraniec
Zenon J. JabŁoński
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, 30059 Kraków, Poland (jablonsk@im.uj.edu.pl; stochel@im.uj.edu.pl; fhszafra@im.uj.edu.pl)
Jan Stochel
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, 30059 Kraków, Poland (jablonsk@im.uj.edu.pl; stochel@im.uj.edu.pl; fhszafra@im.uj.edu.pl)
Franciszek Hugon Szafraniec
Affiliation:
Instytut Matematyki, Uniwersytet Jagielloński, ul. Reymonta 4, 30059 Kraków, Poland (jablonsk@im.uj.edu.pl; stochel@im.uj.edu.pl; fhszafra@im.uj.edu.pl)
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Abstract

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We study the problem of finding conditions which guarantee that given operator data propagate under the control of unitary operators. This is a kind of moment problem and the way we solve it is based on unitary dilations. Comparing it with other results in this area, our approach has the advantages of

allowing the data to be unbounded operators,

considering arbitrary dilations, not necessarily regular ones.

The relationship between the moment problem and harmonizable multivariate discrete processes is indicated.

Keywords

Primary 47A2060G60Secondary 44A6047A5760G10systems of contractions with unitary power dilationsvector and operator moment problemsharmonizable multivariate discrete processes
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 689 - 699
Copyright
Copyright © Edinburgh Mathematical Society 2007