Robert Martin, University of Cape Town
“Multipliers between deBranges-Rovnyak subspaces of Drury-Arveson space”
A natural function-theoretic approach to studying the multiplier algebra of vector-valued Drury-Arveson space is to consider the deBranges-Rovnyak reproducing kernel Hilbert spaces K(b) associated to elements b in the closed unit ball of the multiplier algebra (the Schur class).
We will investigate when there is an isometric or injective multiplier from one deBranges- Rovnyak space into another. In particular, our results will characterize the existence of isomet- ric multipliers from K(b1) into K(b2) in the classical case where b1, b2 are contractive analytic functions on the disk, and b1 is an extreme point.