Journal of Operator Theory

Volume 61, Issue 1, Winter 2009 pp. 63-73.

Dominant Taylor spectrum and invariant subspaces

Authors: C. Ambrozie (1) and V. Muller (2)
Author institution: (1) Mathematical Institute AVCR, Zitna 25, 11567 Prague, Czech Republic and Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700-Bucharest, Romania
(2) Mathematical Institute AVCR, Zitna 25, 11567 Prague, Czech Republic

Summary: Let $T=(T_1 ,\ldots ,T_n )$ be a von Neumann $n$-tuple of commuting Hilbert space operators of class $C_{00}$ with dominating Taylor spectrum. Then $T$ has a nontrivial joint invariant subspace. Stronger results can be obtained if $T$ possesses a dilation.

Keywords: Taylor spectrum, Scott Brown technique, dominant spectrum, invariant subspaces.

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