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

Autori
Archbold, Robert, J. ; Gogić, Ilja ; Robert, Leonel

Izvornik
International mathematics research notices (1073-7928) 2023 (2023), 2; 1483-1513

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
C*-algebra ; the Dixmier property ; weak centrality ; tracial state ; commutator ; quasinilpotent element

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA