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Commuting pairs of normal operators. (English) Zbl 1375.47013

Summary: Let \(M\) be a shift invariant subspace in the two variable Hardy space \(H^2(\Gamma_z\times\Gamma_w)\). We study \(\mathcal{M}(M_z)=\{\phi\in H^\infty(\Gamma_z\times \Gamma_w) : \phi M_z\subseteq M_z\}\) where \(M_z=M\ominus zM\). We give several sufficient conditions for \(\mathcal{M}(M_z)=H^\infty(\Gamma_w)\), where \(H^\infty(\Gamma_w)\) is the one variable Hardy space.

MSC:

47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47A60 Functional calculus for linear operators
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Full Text: Euclid

References:

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