Local variants of the Dixmier property and weak centrality for C*-algebras

Robert J Archbold, Ilja Gogic* (Corresponding Author), Leonel Robert

*Corresponding author for this work

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We study variants of the Dixmier property that apply to elements of a unital C*-algebra, rather than to the C*-algebra itself. By a Dixmier element in a C*-algebra we understand one that can be averaged into a central element by means of a sequence of unitary mixing operators. Examples include all self-commutators and all quasinilpotent elements. We do a parallel study of an element-wise version of weak centrality, where the averaging to the centre is done using unital completely positive elementary operators (as in Magajna’s characterization of weak centrality). We also obtain complete descriptions of more tractable sets of elements, where the corresponding averaging can be done arbitrarily close to the centre. This is achieved through several “spectral conditions”, involving numerical ranges and tracial states.
Original languageEnglish
Article number rnab275
Pages (from-to)1483–1513
Number of pages31
JournalInternational Mathematics Research Notices
Issue number2
Early online date20 Oct 2021
Publication statusPublished - 1 Jan 2023


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