Journal of Operator Theory

Volume 40, Issue 2, Fall 1998 pp. 373-384.

Invariant subspaces for doubly commuting contractions with rich Taylor spectrum

Authors: Ernst Albrecht (1), and Marek Ptak (2)
Author institution: (1) Fachbereich Mathematik, Universitaet des Saarlandes, Postfach 1150, D--66041 Saarbrucken, Germany
(2) Institute of Mathematics, University of Agriculture, Krolewska 6, Krakow, Poland

Summary: In the present paper we prove the existence of nontrivial common invariant subspaces for $N$-tuples of doubly commuting contractions with dominating Taylor spectrum for the $H^\infty$ algebra of the polydisc. We also obtain the reflexivity of the WOT-closed subalgebra generated by finite systems of completely non-unitary doubly commuting contractions with dominating essential Taylor spectrum.

Keywords: Invariant subspaces, reflexive operators, $N$-tuple of contractions, Taylor spectrum

Contents Full-Text PDF