Ken Davidson, Department of Pure Mathematics, University of Waterloo
“The functional calculus for commuting d-tuples of operators”
The classical dilation theory of a single operator of norm 1 yields a continuous functional calculus on the disc algebra A(D). However for ‘most’ operators, this can be improved to a weak-∗ continuous functional calculus on H∞(D). For a commuting d-tuple of operators, (T1, . . . , Tn), if we impose a row contractive condition, we obtain a good dilation theory which yields a continuous functional calculus on a certain commutative operator algebra Ad. We will discuss the dual and double dual of Ad, and explain how ‘most’ commuting row contractions have a weak-∗ continuous functional calculus on Md, the algebra of multipliers of Drury- Arveson space, which is the analogue of H∞ in this context.
This is joint work with Rapha ̈el Clouˆatre.