# Wandering vectors and the reflexivity of free semigroup algebras - Mathematics > Operator Algebras

Wandering vectors and the reflexivity of free semigroup algebras - Mathematics > Operator Algebras - Download this document for free, or read online. Document in PDF available to download.

Abstract: A free semigroup algebra S is the weak-operator-closed non-self-adjointoperator algebra generated by n isometries with pairwise orthogonal ranges. Aunit vector x is said to be wandering for S if the set of images of x undernon-commuting words in the generators of S is orthonormal.We establish the following dichotomy: either a free semigroup algebra has awandering vector, or it is a von Neumann algebra. Consequences include thatevery free semigroup algebra is reflexive, and that certain free semigroupalgebras are hyper-reflexive with a very small hyper-reflexivity constant.

Author: ** Matthew Kennedy**

Source: https://arxiv.org/