Multipliers of de Branges-Rovnyak spaces II

Abstract

Given a nonextreme point bof the unit ball of H ^∞, the multipliers of the de Branges-Rovnyak space H(b) lie in an auxiliary space M (ā) ∩ H ^∞, where a is a function in H ^∞ that is associated with b and M (ā) is the range of the Toeplitz operator T _ā on H ². An example is constructed here to show that M (ā) ∩ H ^∞ need not be an algebra. This contrasts with the case wherebis an extreme point, where the analogous auxiliary space is always an algebra.

First author partially supported by NSF grant DMS-9502983