Interpolation by multipliers on certain spaces of analytic functions

Let ℋ be a Hilbert space of analyticfunctions on a planar domain G such that, for each λ in G,the linear functional eλ of evaluation at λ is bounded onℋ. Furthermore, assume that zℋ⊂ℋ andσ(Mz)=G¯ is an M-spectral set for Mz, the operator of multiplication by z. This paper is devoted to the study ofinterpolation by multipliers of the space ℋ and, in particular,the Dirichlet space.