Journal of Operator Theory

Volume 60, Issue 2, Fall 2008 pp. 317-341.

On operator algebras determined by a sequence of operator norms

Authors: Avraham Feintuch (1) and Alexander Markus (2)
Author institution: (1) Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
(2) Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Summary: We consider a family of operators determined by a sequence of operator norms. When the sequence of norms is determined by a single operator the natural question that arises is when the algebra properly contains the commutant of the operator. In this case the existence of invariant subspaces for the algebra is stronger than the existence of hyperinvariant subspaces for the operator.

Keywords: Operator algebras, operator norms, invariant subspace, spectral radius algebra.

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