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- W4301672693 abstract "The problem of expressing a selfadjoint element that is zero on every bounded trace as a finite sum (or a limit of sums) of commutators is investigated in the setting of C*-algebras of finite nuclear dimension. Upper bounds -- in terms of the nuclear dimension of the C*-algebra -- are given for the number of commutators needed in these sums. An example is given of a simple, nuclear C*-algebra (of infinite nuclear dimension) with a unique tracial state and with elements that vanish on all bounded traces and yet are badly approximated by finite sums of commutators. Finally, the same problem is investigated on (possibly non-nuclear) simple unital C*-algebras assuming suitable regularity properties in their Cuntz semigroups." @default.
- W4301672693 created "2022-10-05" @default.
- W4301672693 creator A5045947995 @default.
- W4301672693 date "2013-09-02" @default.
- W4301672693 modified "2023-09-28" @default.
- W4301672693 title "Nuclear dimension and sums of commutators" @default.
- W4301672693 doi "https://doi.org/10.48550/arxiv.1309.0498" @default.
- W4301672693 hasPublicationYear "2013" @default.
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