Monotone Matrix functions in several variables

Monotone Matrix functions in several variables

Tue, 23/02/2010
17:00 		John McCarthy (Washington Univ St Louis and Trinity College Dublin) Functional Analysis Seminar Add to calendar L3
Monotone Matrix functions in several variables
In 1934, K. Loewner characterized functions that preserve matrix inequalities, i.e. those f with the property that whenever A and B are self-adjoint matrices of the same dimension, with $ A \leq B $, then $ f(A) \leq f(B) $. In this talk, I shall discuss how to characterize monotone matrix functions of several variables, namely functions f with the property that if $ A = (A_1, \dots , A_n) $ is an n-tuple of commuting self-adjoint matrices, and $ B = (B_1, \dots, B_n) $ is another, with each $ A_i \leq B_i $, then $ f(A) \leq f(B) $.