Journal of Operator Theory

Volume 42, Issue 2, Fall 1999 pp. 405-428.

Commutative radical operator algebras

Authors: Justin R. Peters (1), and Warren R. Wogen (2)
Author institution: (1) Mathematics Department, Iowa State UniversityAmes, IA 50011, USA
(2) Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, USA

Summary: Let $A$ be a norm-closed operator algebra which is radical; that is, each element in $A$ is quasinilpotent. We consider the case when such algebras satisfy the stronger condition of being uniformly topologically nil. In particular, we study this question when $A$ is generated by a quasinilpotent weighted shift or by the Volterra operator.

Keywords: radical operator algebra, quasinilpotent, uniformly topologically nil, weighted shift, Volterra operator

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