Past Functional Analysis Seminar

23 February 2010
17:00
to
18:37
Abstract
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 $f(A) \leq f(B)$.
  • Functional Analysis Seminar

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