Texas A&M University, Department of
Mathematics, 216 Milner Hall, 8th of September 2004, 3:00-3:50
Groups and Dynamics Seminar
Characterization of
amenable C*-algebras by their similarity degree
Gilles Pisier of Texas A&M
University
The similarity degree is the smallest exponent of the growth function
associated to the similarity problem for bounded homomorphisms from an
operator algebra A into B(H). The author proved previously that it is
an integer and that this integer is equal to the ``length" (in a
suitable sense) of A. In this talk we will present our very recent
result (improving a previous attempt) that if A is a C*-algebra
(infinite dimensional) then its length is equal to 2 iff it is amenable
(=nuclear). This is the C*-algebraic analogue of a previous result of
the author for the length of amenable groups.