Journal of Operator Theory

Volume 45, Issue 2, Spring 2001 pp. 413-443.

Invariant subspaces for commuting contractions

Authors: Jorg Eschmeier
Author institution: Fachbereich Mathematik, Universitaet des Saarlandes, Postfach 15 11 50, D--66041 Saarbrucken, Germany

Summary: It is shown that each finite commuting system of contractions which possesses a unitary dilation and for which the Harte spectrum is dominating in the open unit polydisc possesses non-trivial joint invariant subspaces. Since by a well-known result of Ando each commuting pair of contractions admits a unitary dilation, we obtain in particular that each commuting pair of contractions with dominating Harte spectrum in the bidisc possesses non-trivial joint invariant subspaces.

Keywords: Invariant subspaces, commuting contractions, Harte spectrum, dual operator algebras, Henkin measures

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