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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/







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