## 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

### Keywords:

Fuglede-Putnam theorem; normal elements; commutativity
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### References:

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