ABSTRACT
ROGER D. NUSSBAUM Mathematics Department, Rutgers University, New Brunswick, New Jersey
There is an enormous classical literature concerning what might be called "means and their iterates." The survey article [7] by Arazy, Claesson, Janson and Peetre provides an excellent bibliography. In this section we shall review some of these classical examples, particularly the arithmetic-geometric mean. The main body of the paper comprises results and open questions related to the problem of extending the classical means, particularly the arithmetic-geometric mean, to the case that the variables are (noncommuting), positive semi-definite, self-adjoint bounded linear operators on a Hilbert space.
