Eli Shamovich, Department of Pure Mathematics, University of Waterloo
"Noncommutative kernels, multipliers, and the Fock space"
This time we will discuss noncommutative reproducing kernels, that are a way to unify two concepts, cp maps and reproducing kernels. We will show that the Fock space is a noncommutative reproducing kernels Hilbert space (nc-RKHS). We will discuss the multiplier algebra of an nc-RKHS and show that it is always a dual operator algebra. In the case of the Fock space, this algebra is, on the one hand, the algebra of bounded nc functions on the free ball and on the other, the free semigroup algebra of Davidson and Pitts. Lastly, we will discuss the complete Nevanlinna-Pick property of nc reproducing kernels and show that the Fock space has it.
MC 5479