Factoring in Non-commutative Analytic Toeplitz Algebras

Details Factoring in Non-commutative Analytic Toeplitz Algebras Factoring in Non-commutative Analytic Toeplitz Algebras

2003-09-23

arxiv.org/abs/math/0309382v1

J. Operator Theory 45 (2001), 175-193

Mathematics

Operator Algebras

23 pages, preprint version

Scientific paper

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 $H^\infty$ 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.

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