On the Radius of Comparison of a Commutative C*-algebra

Abstract

Abstract.Let X be a compact metric space. A lower bound for the radius of comparison of the C*-algebra C(X) is given in terms of dimQ X, where dimQ X is the cohomological dimension with rational coefficients. If dimQX = dim X = d, then the radius of comparison of the C*-algebra C(X) is maxf0; (d/1)=2/1g if d is odd, and must be either d=2/1 or d=2/2 if d is even (the possibility d=2 - 1 does occur, but we do not know if the possibility d=2 - 2 can also occur).