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A local lifting theorem for subnormal operators

Authors: Witold Majdak, Zoltán Sebestyén, Jan Stochel and James E. Thomson
Journal: Proc. Amer. Math. Soc. 134 (2006), 1687-1699
MSC (2000): Primary 47B20; Secondary 47A20
Published electronically: December 2, 2005
MathSciNet review: 2204281
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Abstract: Criteria for the existence of lifts of operators intertwining subnormal operators are established. The main result of the paper reduces lifting questions for general subnormal operators to questions about lifts of cyclic subnormal operators. It is shown that in general the existence of local lifts (i.e. those coming from cyclic parts) for a pair of subnormal operators does not imply the existence of a global lift. However this is the case when minimal normal extensions of subnormal operators in question are star-cyclic.

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Witold Majdak
Affiliation: Faculty of Applied Mathematics, AGH Science and Technology University, Al. Mickiewicza 30, 30-059 Kraków, Poland

Zoltán Sebestyén
Affiliation: Department of Applied Analysis, Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/c, Hungary

Jan Stochel
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, 30-059 Kraków, Poland

James E. Thomson
Affiliation: Department of Mathematics, 460 McBryde Hall, Virginia Tech, Blacksburg, Virginia 24061-0123

Keywords: Subnormal operator, minimal normal extension, star-cyclic minimal normal extension, lift of intertwining operator, lifting commutant theorem
Received by editor(s): July 8, 2004
Received by editor(s) in revised form: January 10, 2005
Published electronically: December 2, 2005
Additional Notes: The research of the third author was supported by KBN grant 2 P03A 037 024.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society

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