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Domination by positive disjointly strictly singular operators

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Flores Álvarez, Julio and Hernández, Francisco L. (2001) Domination by positive disjointly strictly singular operators. Proceedings of the American Mathematical Society, 129 (7). pp. 1979-1986. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/2001-129-07/S0002-9939-00-05948-7/S0002-9939-00-05948-7.pdf


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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 --> E is dominated by a disjointly strictly singular operator, then S-2 is disjointly strictly singular.


Item Type:Article
Uncontrolled Keywords:Compact operators; Banach lattices
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16043
Deposited On:24 Jul 2012 09:56
Last Modified:09 Aug 2018 11:48

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