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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1979-1986
- MSC (2000): Primary 47B65, 46B42
- DOI: https://doi.org/10.1090/S0002-9939-00-05948-7
- MathSciNet review: 1825905