1999/03/23 by Y. A. Abramovich, Abramovich, Y. A., Charalambos D. Aliprantis +7
Mathematics · #46E30 #47B38 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46E30 #msc:47B38
paper · pdf · doi:10.48550/arxiv.math/9903139
To appear in Indag. Math., 12 pages
arxiv created 1999/03/23 · openalex publication_date 1999/03/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Answering 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 Lp-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.