Simultaneous averaging to zero by unitary mixing operators

2020/12/04 by Chand, Abhinav, Robert, Leonel, Sutradhar, Arindam
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2012.02830

Abstract

We show that if every element a vector subspace of a C*-algebra can be averaged to zero by means of unitary mixing operators, then all the elements of the subspace can be simultaneously averaged to zero by a net of unitary mixing operators. Moreover, such subspaces admit a simple description in terms of commutators and kernels of states on the C*-algebra. We apply this result to center-valued expectations in C*-algebras with the Dixmier property.

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