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

 

Domination by positive disjointly strictly singular operators


Authors: Julio Flores and Francisco L. Hernández
Journal: Proc. Amer. Math. Soc. 129 (2001), 1979-1986
MSC (2000): Primary 47B65, 46B42
Published electronically: November 22, 2000
MathSciNet review: 1825905
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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 $S:E\to E$ is dominated by a disjointly strictly singular operator, then $S^2$ is disjointly strictly singular.


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Additional Information

Julio Flores
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Email: jflores@sunam1.mat.ucm.es

Francisco L. Hernández
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Email: pacoh@eucmax.sim.ucm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05948-7
PII: S 0002-9939(00)05948-7
Received by editor(s): October 14, 1999
Published electronically: November 22, 2000
Additional Notes: This work was partially supported by DGES PB97-0240
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society