Domination by positive disjointly strictly singular operators

Flores, Julio; Hernández, Francisco

doi:10.1090/S0002-9939-00-05948-7

Domination by positive disjointly strictly singular operators
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by Julio Flores and Francisco L. Hernández PDF

Proc. Amer. Math. Soc. 129 (2001), 1979-1986 Request permission

Abstract:

We prove that each positive operator from a Banach lattice $E$ to a Banach lattice $F$ with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on $F$ is order continuous. We prove as well that if $S:E\to E$ is dominated by a disjointly strictly singular operator, then $S^2$ is disjointly strictly singular.

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