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Abstract
A free semigroup algebra 
is the weak-operator-closed (non-self-adjoint) operator algebra generated by n isometries with pairwise orthogonal ranges. A unit vector x is said to be wandering for if the set of images of x under words in the generators of is orthonormal.
We establish the following dichotomy: either a free semigroup algebra has a wandering vector, or it is a von Neumann algebra. Consequences include that every free semigroup algebra is reflexive, and that certain free semigroup algebras are hyper-reflexive with a very small hyper-reflexivity constant.
Received: 2009-09-18
Revised: 2009-10-31
Published Online: 2010-12-14
Published in Print: 2011-April
© Walter de Gruyter Berlin · New York 2011
