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Journal of Operator Theory

Volume 37, Issue 1, Winter 1997  pp. 3-21.

Smoothing techniques in C*-algebras theory

Authors: Terry A. Loring (1) and Gert K. Pedersen (2)
Author institution:(1) Dept. of Math, and Statistics, University of New Mexico, Albuquerque, NM 87131, U.S.A. (2) Mathematics Institute, University of Copenhagen, 5 Universitetsparken, DK-2100 Copenhagen Ø, DENMARK

Summary: We show that any algebraic element in a C*-algebra A can be approximated by a smooth algebraic element, with the same minimal polynomial. By a smooth element we mean an element of a given dense subalgebra $A_\infty$ that is closed under $C^\infty$ functional calculus. Smoothing results for a variety of other C*-relations are obtained. These serve to prove the density of the smooth homomorphisms in hom(CM_n, A). From this, smoothing results in mod-p K-theory may be derived. We also prove two closure properties for stable, smoothable relations.

Keywords: C*-algebra, algebraic element, perturbation, stable relations, smoothing.

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