2021/05/31 by R. J. Archbold, Archbold, Robert J., Ilja Gogić +3 · 1 citation
Materials Science · Mathematics · #46L05 #47B47 #Advanced Operator Algebra Research #FOS: Mathematics #Lanthanide and Transition Metal Complexes #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2106.00098
openalex publication_date 2021/05/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We study variants of the Dixmier property that apply to elements of a unital\nC*-algebra, rather than to the C*-algebra itself. By a Dixmier element in a\nC*-algebra we understand one that can be averaged into a central element by\nmeans of a sequence of unitary mixing operators. Examples include all\nself-commutators and all quasinilpotent elements. We do a parallel study of an\nelement-wise version of weak centrality, where the averaging to the centre is\ndone using unital completely positive elementary operators (as in Magajna's\ncharacterization of weak centrality). We also obtain complete descriptions of\nmore tractable sets of elements, where the corresponding averaging can be done\narbitrarily close to the centre. This is achieved through several "spectral\nconditions", involving numerical ranges and tracial states.\n