#### Event Title

The functional calculus for commuting row contractions

Brown Hall 100

#### Start Date

7-22-2016 9:40 AM

#### End Date

22-7-2016 10:30 AM

#### Description

A commuting row contraction is a $d$-tuple of commuting operators $T_1,\dots,T_d$ such that $\sum_{i=1}^d T_iT_i^* \le I$. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers $\A_d$ on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-$*$ continuous functional calculus on the full multiplier algebra. In particular, we show that completely non-unitary row contractions are always absolutely continuous, in direct parallel with the case of a single contraction. This is based on the detailed structure of the dual space of $\A_d$. Finally, we consider refinements of this question for row contractions that are annihilated by a given ideal. This is joint work with Rapha\"el Clou\^atre.

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Jul 22nd, 9:40 AM Jul 22nd, 10:30 AM

The functional calculus for commuting row contractions

Brown Hall 100

A commuting row contraction is a $d$-tuple of commuting operators $T_1,\dots,T_d$ such that $\sum_{i=1}^d T_iT_i^* \le I$. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers $\A_d$ on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-$*$ continuous functional calculus on the full multiplier algebra. In particular, we show that completely non-unitary row contractions are always absolutely continuous, in direct parallel with the case of a single contraction. This is based on the detailed structure of the dual space of $\A_d$. Finally, we consider refinements of this question for row contractions that are annihilated by a given ideal. This is joint work with Rapha\"el Clou\^atre.