Operator power means in the view of fixed points

DOI10.1007/s11785-022-01298-5OpenAlexW4308426415MaRDI QIDQ2679099

Sejong Kim

Publication date: 19 January 2023

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-022-01298-5

zbMATH Keywords

Banach fixed point theorempower meanRényi divergenceThompson metric

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Positive linear operators and order-bounded operators (47B65)

Cites Work

• Operator power means due to Lawson-Lim-Pálfia for \(1 < t < 2\)
• Nonexpansiveness of the resolvent average
• Matrix power means and the Karcher mean
• Operator means deformed by a fixed point method
• Convexity of the geodesic distance on spaces of positive operators
• The quasi-arithmetic means and Cartan barycenters of compactly supported measures
• Geometric means
• Tensor product and Hadamard product for the Wasserstein means
• The Rényi power means of matrices
• The Ando-Hiai inequalities for the solution of the generalized Karcher equation and related results
• Metric convexity of symmetric cones
• Karcher means and Karcher equations of positive definite operators
• An effective matrix geometric mean satisfying the Ando–Li–Mathias properties
• Inequalities between means of positive operators
• On Certain Contraction Mappings in a Partially Ordered Vector Space

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