Abstract
For μ a compactly supported measure on ℂ, we construct a mutually absolutely continuous measure ν so thatP 2(ν) has analytic bounded point evaluations, and the operator of multiplication byz onP 2(ν) has every invariant subspace hyperinvariant. We also construct an equivalent measure σ so thatR 2(K, σ) has as analytic bounded point evaluations precisely the interior of the set of weak-star continuous point evaluations ofR ∞(K, μ). In the course of the proof, we classify weak-star closed super-algebras ofR ∞(K, μ) whenR(K) is hypo-Dirichlet.
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McCarthy, J.E. Analytic structures for subnormal operators. Integr equ oper theory 13, 251–270 (1990). https://doi.org/10.1007/BF01193759
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DOI: https://doi.org/10.1007/BF01193759