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Domination by positive disjointly strictly singular operators

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dc.contributor.authorFlores Álvarez, Julio
dc.contributor.authorHernández, Francisco L.
dc.date.accessioned2023-06-20T16:56:18Z
dc.date.available2023-06-20T16:56:18Z
dc.date.issued2001
dc.description.abstractWe 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.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipDGES
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16043
dc.identifier.doi10.1090/S0002-9939-00-05948-7
dc.identifier.issn0002-9939
dc.identifier.officialurlhttp://www.ams.org/journals/proc/2001-129-07/S0002-9939-00-05948-7/S0002-9939-00-05948-7.pdf
dc.identifier.relatedurlhttp://www.ams.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57468
dc.issue.number7
dc.journal.titleProceedings of the American Mathematical Society
dc.language.isoeng
dc.page.final1986
dc.page.initial1979
dc.publisherAmerican Mathematical Society
dc.relation.projectIDPB97-0240
dc.rights.accessRightsrestricted access
dc.subject.cdu517.98
dc.subject.cdu517.982.22
dc.subject.keywordCompact operators
dc.subject.keywordBanach lattices
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleDomination by positive disjointly strictly singular operators
dc.typejournal article
dc.volume.number129
dcterms.referencesY. A. Abramovich, Weakly compact sets in topological K-spaces, Teor. Funkcii Funkional. Anal. i Prilozen 15 (1972), 27-35. C.D. Aliprantis and O. Burkinshaw, Positive compact operators on Banach lattices, Math. Z. 174 (1980), 289-298. On weakly compact operators on Banach lattices, Proc. Amer. Math. Soc. 83 (1981), 573-578. Positive operators, Academic Press, 1985. P.G. Dodds and D.H. Fremlin, Compact operators in Banach lattices, Israel J. of Math. 34 (1979), 287-320. N. Dunford and J.T. Schwartz, Linear Operators. Part I, General Theory, Pure and applied Mathematics, vol. VII, Interscience, New York, 1958. A. García Del Amo, F. L. Hernández, and C. Ruiz, Disjointly strictly singular operators and interpolation, Proc. Royal Soc. of Edinburgh 126A (1996), 1011-1026. F. L. Hernández, Disjointly Strictly-Singular Operators in Banach Lattices, Proc. 18 Winter School on Abstract Analysis (Srni). Acta Universitatis Carolinae-Mathematica et Physica 31(1990), 35-40. F. L. Hernández and B. Rodríguez-Salinas, On lp-complemented copies in Orlicz spaces II, Israel J. of Math. 68 (1989), 27-55. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer-Verlag, 1977. Classical Banach Spaces II, Springer-Verlag, 1979. P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, 1991. A.W. Wickstead, Extremal structure of cones of operators, Quart. J. Math. Oxford Ser. (2) 32 (1981), 239-253. Converses for the Dodds-Fremlin and Kalton-Saab theorems, Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. A. C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, 1983.
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