Journal of Operator Theory

Volume 45, Issue 1, Winter 2001 pp. 175-193.

Non-commutative analytic Toeplitz algebras

Authors: David W. Kribs
Author institution: Pure Mathematics Department, University of Waterloo, Waterloo, Ontario N2L-3G1, Canada

Summary: The non-commutative analytic Toeplitz algebra is the $\rm WOT$-closed algebra generated by the left regular representation of the free semigroup on $n$ generators. The structure theory of contractions in these algebras is examined. Each is shown to have an $H^\infty$ functional calculus. The isometries defined by words are shown to factor only as the words do over th e unit ball of the algebra. This turns out to be false over the full algebra. The natural identification of $\rm WOT$-closed left ideals with invariant subspaces of the algebra is shown to hold only for a proper subcollection of the subspace s.

Keywords: Analytic Toeplitz algebra, left regular representation, isometric dilation

Contents Full-Text PDF