FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 8, PAGES 213-227

**Unitarily covariant maps in approximately finite-dimensional
$C$*-algebras**

T. Shulman

Abstract

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We consider maps defined on a real space $A$_{sa} of all
self-adjoint elements of a $C$*-algebra $A$ commuting with the
conjugation by unitaries: $F(u$*au) = u^{*}F(a)u for any
$a$Î A_{sa},
$u$Î U(A).
In the case where $A$ is a full matrix
algebra, there is a functional realization of these maps (in
terms of multivariable functions) and analytical properties of these
maps can be expressed in terms of corresponding functions.
In the present work, these results are generalized to the class of
uniformly hyperfinite $C$*-algebras and to
the algebra of all compact operators in a Hilbert space.

Location: http://mech.math.msu.su/~fpm/eng/k07/k078/k07813h.htm

Last modified: June 13, 2008