Following the Trail of the Operator Geometric Mean
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Publication:5152770
DOI10.1007/978-3-030-53305-2_10OpenAlexW3097857792MaRDI QIDQ5152770
Publication date: 27 September 2021
Published in: Trends in Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-030-53305-2_10
operator monotone functiongeometric meanoperator meannonpositively curved metric spacescontractive barycentric map
General theory of (C^*)-algebras (46L05) Positive linear operators and order-bounded operators (47B65) Convex sets and cones of operators (47L07) Operator means involving linear operators, shorted linear operators, etc. (47A64)
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Cites Work
- Unnamed Item
- Matrix power means and the Karcher mean
- Noncommutative geometric means
- Riemannian geometry and matrix geometric means
- Means of positive linear operators
- Geometric means
- Existence, uniqueness and an ODE approach to the \(L^1\)-Karcher mean
- Existence and uniqueness of the Karcher mean on unital \(C^\ast\)-algebras
- An extended Lie--Trotter formula and its applications
- Karcher means and Karcher equations of positive definite operators
- An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
- Upper and lower bounds for the arithmetic-geometric-harmonic means of positive definite matrices
- The Geometric Mean, Matrices, Metrics, and More
- Contractive barycentric map
- A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices