Oral Comprehensive Seminar

Adam Dor On, Pure Mathematics, University of Waterloo

"Absolute continuity and wandering vectors in Free semigroup algebras"

We sketch Kennedy's proof of the existence of a wandering vector for  
an analytic / type L free semigroup algebra, drawing connections with  
absolute continuity. We then discuss a strengthening of this result,  
also due to Kennedy, that unifies many notions in the theory of free  
semigroup algebras, and allowed for a Wold decomposition of isometric  
tuples into a direct sum of a unilateral shift, an absolute continuity  
unitary and a singular unitary.