Invariant subspaces of super left-commutants

Gessesse, Hailegebriel

doi:10.1090/S0002-9939-08-09673-1

Invariant subspaces of super left-commutants
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by Hailegebriel E. Gessesse PDF

Proc. Amer. Math. Soc. 137 (2009), 1357-1361 Request permission

Abstract:

For a positive operator $Q$ on a Banach lattice, one defines $\langle Q]=\{T\geq 0 : ~TQ\leq QT\}$ and $[Q\rangle =\{T\geq 0 : TQ\geq QT\}$. There have been several recent results asserting that, under certain assumptions on $Q$, $[Q\rangle$ has a common invariant subspace. In this paper, we use the technique of minimal vectors to establish similar results for $\langle Q]$.

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