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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Invariant subspaces of finite codimension for measures with thin support


Author: T. T. Trent
Journal: Proc. Amer. Math. Soc. 109 (1990), 369-374
MSC: Primary 47B20; Secondary 46E20, 46G99, 47A15
MathSciNet review: 1010003
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Abstract: A simple proof that $ {M_z}$ on $ {P^2}(\mu )$ has a nontrivial invariant subspace is given. If $ {P^2}(\mu ) \ne {L^2}(\mu )$ and if $ \mu $ has "thin" support, then $ {P^2}(\mu )$ has bounded point evaluations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1010003-8
PII: S 0002-9939(1990)1010003-8
Keywords: Subnormal operator, invariant subspace, bounded point evaluation
Article copyright: © Copyright 1990 American Mathematical Society