Strong law of large numbers for generalized operator means

Strong limit theorems (60F15) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Cites Work

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Weak convergence and Banach space-valued functions: improving the stability theory of Feynman's operational calculi
Monotonicity of the matrix geometric mean
Lipschitz properties of convex functions
Monotonic properties of the least squares mean
Matrix power means and the Karcher mean
Strong law of large numbers for the \(L^1\)-Karcher mean
Riemannian geometry and matrix geometric means
Operator means of probability measures and generalized Karcher equations
Invariance principles in probability for triangular arrays of B-valued random vectors and some applications
The stochastic order of probability measures on ordered metric spaces
Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature
A multiplicative ergodic theorem and nonpositively curved spaces
Ordered probability spaces
Existence, uniqueness and an ODE approach to the \(L^1\)-Karcher mean
The contraction rate in Thompson's part metric of order-preserving flows on a cone -- application to generalized Riccati equations
Convergence rate of incremental subgradient algorithms
Karcher means and Karcher equations of positive definite operators
No dice: a deterministic approach to the Cartan centroid
Optimization and nonsmooth analysis
Flow-invariant sets and differential inequalities in normed spaces^†
Real Analysis and Probability
Perspectives of matrix convex functions
Weighted means and Karcher equations of positive operators
Weighted deterministic walks for the least squares mean on Hadamard spaces
Symmetric spaces with convex metrics
Convergence of weighted averages of random variables revisited
On Certain Contraction Mappings in a Partially Ordered Vector Space
Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
Ergodic theorem in CAT(0) spaces in terms of inductive means
Optimal Transport

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