2003/09/23 by David W. Kribs
Mathematics · #math.OA #msc:47D25
published as J. Operator Theory 45 (2001), 175-193 · 23 pages, preprint version
arxiv created 2003/09/23 · arxiv updated 2009/12/01
The non-commutative analytic Toeplitz algebra is the weak operator topology 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^∞ functional calculus. The isometries defined by words are shown to factor only as the words do over the unit ball of the algebra. This turns out to be false over the full algebra. The natural identification of weakly closed left ideals with invariant subspaces of the algebra is shown to hold only for a proper subcollection of the subspaces.