A Characterization of Compact-friendly Multiplication Operators

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dc.creatorAbramovich, Y. A.
dc.creatorAliprantis, C. D.
dc.creatorBurkinshaw, O.
dc.creatorWickstead, A. W.
dc.date1999-03-23
dc.date.accessioned2026-07-07T05:28:27Z
dc.date.available2026-07-07T05:28:27Z
dc.descriptionAnswering in the affirmative a question posed in [Y.A.Abramovich, C.D.Aliprantis and O.Burkinshaw, Multiplication and compact-friendly operators, Positivity 1 (1997), 171--180], we prove that a positive multiplication operator on any $L_p$-space (resp. on a $C(Ω)$-space) is compact-friendly if and only if the multiplier is constant on a set of positive measure (resp. on a non-empty open set). In the process of establishing this result, we also prove that any multiplication operator has a family of hyperinvariant bands -- a fact that does not seem to have appeared in the literature before. This provides useful information about the commutant of a multiplication operator.
dc.descriptionTo appear in Indag. Math., 12 pages
dc.identifierhttps://arxiv.org/abs/math/9903139
dc.identifierhttp://arxiv.org/abs/math/9903139
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78261
dc.subjectFunctional Analysis
dc.subject47B38; 46E30
dc.titleA Characterization of Compact-friendly Multiplication Operators
dc.typetext

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