2012/10/11 by Fedor Sukochev, Sukochev, Fedor, Alexandr Usachev +3
Mathematics · #46L52 #58B34 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L52 #msc:58B34
paper · pdf · doi:10.48550/arxiv.1210.3397
arxiv created 2012/10/11 · openalex publication_date 2012/10/11 · arxiv updated 2012/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we prove that the classes of Dixmier and Connes-Dixmier traces differ even on the Dixmier ideal \mathcal M1,∞. We construct a Marcinkiewicz space \mathcal Mψ and a positive operator T∈ \mathcal Mψ which is Connes-Dixmier measurable but which is not Dixmier measurable.