Some subnormal operators not in A2


AbstractBercovici, Foias, and Pearcy have defined a decreasing sequence of classes of operators, An, 1 ⩽ n < ℵ0. If A denotes area measure on the disc D and if S = Mz on P2(dA) then S ϵ Aℵ0; on the other hand, if μ = ¦dz¦Γ + dA for some arc Γ on ∂D, we show Mz on P2(μ) is an element of A1/A2, while its minimal normal extension, Mz on L2(μ), is in Aℵ0. Let S be a subnormal operator whose minimal normal extension has scalar valued spectral measure μ such that P∞(μ) = H∞(D). If there exist λ ϵ D and ƒ ϵH∞(D) so that ¦ƒ(λ)¦ > ∥ƒ∥μD we give a condition sufficient for S to be a member of A1A2

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Elsevier - Publisher Connector

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