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INVARIANT SUBSPACES FOR SOME FAMILIES OF UNBOUNDED SUBNORMAL OPERATORS

Published online by Cambridge University Press:  01 May 2003

E. ALBRECHT  and
F.-H. VASILESCU
E. ALBRECHT
Affiliation:
Fachrichtung 6.1 – Mathematik, Universität des Saarlandes, Postfach 15 11 50, D-66041 Saarbrücken, Germany e-mail: ernstalb@math.uni-sb.de
F.-H. VASILESCU
Affiliation:
U.F.R. de Mathématiques, Université des Sciences et Technologies de Lille, U.M.R. du C.N.R.S. 8524, 59655 Villeneuve d'Ascq Cedex, France e-mail: fhvasil@gat.univ-lillel.fr
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Abstract

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Extending results and methods of Thomson and Trent, we prove the existence of non trivial quasi-invariant subspaces for subnormal families of unbounded operators having sufficiently rich domains. In some special cases, proper invariant subspaces are obtained.

Keywords

47A1547B20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 53 - 67
Copyright
2003 Glasgow Mathematical Journal Trust

Footnotes

This work has been prepared while the second named author was a guest of the University of the Saarland as a Humboldt Fellow. He would like to express his gratitude to the Alexander von Humboldt-Foundation for its support and to the University of the Saarland for its hospitality.