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

 

Representations of $ {\rm Alg}\,{\rm Lat}(T)$


Author: Jörg Eschmeier
Journal: Proc. Amer. Math. Soc. 117 (1993), 1013-1021
MSC: Primary 47B20; Secondary 47A11, 47A15, 47B40
MathSciNet review: 1152979
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Abstract: For a hyponormal operator $ T$ with the property that the boundary of the essential spectrum is of planar Lebesgue measure zero, it is proved that the operator algebra $ \operatorname{AlgLat} (T)$ generated by the invariant subspace lattice of $ T$ is commutative. If in addition $ T$ is a pure hyponormal operator, then $ \operatorname{AlgLat} (T)$ is shown to be contained in the bicommutant of $ T$. These are particular cases of more general results obtained for restrictions and quotients of operators decomposable in the sense of Foiaş.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1152979-7
PII: S 0002-9939(1993)1152979-7
Article copyright: © Copyright 1993 American Mathematical Society