Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals

2016/08/25 by Dan-Virgil Voiculescu, Voiculescu, Dan-Virgil
Mathematics · #47A55 #47L20 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Primary: 47L50 #Secondary: 46B20 #math.FA #math.OA #msc:46B20 #msc:47A55 #msc:47L20 #msc:47L50

paper · pdf · doi:10.48550/arxiv.1608.07228

12 pages preliminary version

arxiv created 2016/08/25 · openalex publication_date 2016/08/25 · arxiv updated 2016/08/26 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove an analogue of the Lebesgue decomposition for continuous functionals on the commutant modulo a reflexive normed ideal of an n-tuple of hermitian operators for which there are quasicentral approximate units relative to the normed ideal. Using results of Godefroy-Talagrand and Pfitzner we derive from this strong uniqueness of the predual of such a commutant modulo a normed ideal.

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