## On the reflexivity of operators on function spaces.(English)Zbl 0806.47026

Summary: Let $$\Omega$$ be a bounded plane domain. Sufficient conditions are given so that an operator $$T$$ in the Cowen-Douglas class $${\mathcal B}_ n(\Omega)$$ is reflexive. The operator $$M_ z$$ of multiplication by $$z$$ on a Hilbert space of functions analytic on a finitely connected domain $$\Omega$$ is shown to be reflexive whenever $$\sigma(M_ z)= \overline\Omega$$ is a spectral set.

### MSC:

 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 46E20 Hilbert spaces of continuous, differentiable or analytic functions 47A25 Spectral sets of linear operators
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### References:

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