Can I read Existence and Uniqueness of the Karcher Mean on Unital $C^*$-algebras on EtoBox?

Existence and Uniqueness of the Karcher Mean on Unital $C^*$-algebras by Lawson, Jimmie is a scholarly article available to read on EtoBox.

What is Existence and Uniqueness of the Karcher Mean on Unital $C^*$-algebras about?

The Karcher mean on the cone $\Omega$ of invertible positive elements of the $C^*$-algebra $\mathcal{B}(E)$ of bounded operators on a Hilbert space $E$ has recently been extended to a contractive barycentric map on the space of $L^1$- probability measures on $\Omega$. In this paper we first show that the barycenter satisfies the Karcher equation and then establish the uniqueness of the solution. Next we establish that the Karcher mean is real analytic in each of its coordinates, and use this fact to show that boththe Karcher mean and Karcher barycenter map exist and are unique on any unital $C^*$-algebra. The proof depends crucially on a recent result of the author giving a converse of the inverse function theorem.

Author

Lawson, Jimmie

Published

2019

Language

EN