Journal of Operator Theory

Volume 42, Issue 1, Summer 1999 pp. 37-76.

Algebras of subnormal operators on the unit ball

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

Summary: In this paper we show that each subnormal

$n$ -tuple

$T\in L(H)^n$ with the property that the Taylor spectrum of

$T$ is contained in the closed Euclidean unit ball and is dominating in the open ball, is reflexive. The proof is based on the observation that the dual algebra generated by

$T$ possesses the factorization property

$({\bbb A}_{1,\aleph_0})$ . The same results are shown to hold for subnormal tuples that possess an isometric

${\rm w}^*$ -continuous

$H^\infty$ -functional calculus over the unit ball. Thus we extend a result of Olin and Thomson on the reflexivity of arbitrary single subnormal operators to the case of subnormal systems with rich spectrum in the Euclidean unit ball.

Contents Full-Text PDF