Each hyperinvariant subspace for a multiplication operator is spectral

Huang, Sen Zhong

doi:10.1090/S0002-9939-1989-0975657-2

Each hyperinvariant subspace for a multiplication operator is spectral
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by Sen Zhong Huang

Proc. Amer. Math. Soc. 106 (1989), 1057-1061

DOI: https://doi.org/10.1090/S0002-9939-1989-0975657-2

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Abstract:

We consider multiplication operators on general separable complex ${L^p}$-spaces, for $1 \leq p < + \infty$, and obtain the result announced in the title. Moreover, a result of Douglas and Pearcy on normal operators is given an alternate proof.

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