Commutants, Reducing Subspaces and von Neumann Algebras Associated with Multiplication Operators

Let Ω be a bounded domain of ℂ ⁿ and let ℋ be a Hilbert space consisting of holomorphic functions on Ω. If for every λ ∈ Ω, the map E λ : f → f ( λ ) , f ∈ ℋ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781351045551/4730f38a-3e35-40e9-9674-aa9748370ac3/content/eq492.tif"/>