Abstract
Evidence is assembled supporting the conjecture that a normal element of a simple C*-algebra is determined up to approximate unitary equivalence by the following elementary invariants: the spectrum of the element, the measure on its spectrum arising from each trace (or quasitrace) on the algebra, the K0-class of the spectral projection associated to each compact component of the spectrum together with the information whether the sum of these projections is the unit of the C*-algebra (if there is one), and, finally, the K1-class of the resolvent of the element over each bounded component of the complement of the spectrum. (In the case of a self-adjoint element the last invariant is trivial, and in the case of a unitary element it is the K1-class of the unitary itself.)
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Elliott, G.A. (1994). Normal Elements of a Simple C*-Algebra. In: Curto, R.E., Jørgensen, P.E.T. (eds) Algebraic Methods in Operator Theory. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0255-4_13
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DOI: https://doi.org/10.1007/978-1-4612-0255-4_13
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