Representations of 𝐴𝑙𝑔𝐿𝑎𝑡(𝑇)

Eschmeier, Jörg

doi:10.1090/S0002-9939-1993-1152979-7

Representations of $\textrm {Alg} \textrm {Lat}(T)$
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Proc. Amer. Math. Soc. 117 (1993), 1013-1021 Request permission

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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