CONNECTIONS ON STATISTICAL MANIFOLDS OF DENSITY OPERATORS BY GEOMETRY OF NONCOMMUTATIVE Lp-SPACES

DOI10.1142/S0219025799000096zbMath1040.46502MaRDI QIDQ4269404

Paolo Gibilisco, Tommaso Isola

Publication date: 29 November 1999

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10)

Related Items (16)

Examples of the application of nonparametric information geometry to statistical physics ⋮ Information geometry formalism for the spatially homogeneous Boltzmann equation ⋮ DUALITY, MONOTONICITY AND THE WIGNER–YANASE–DYSON METRICS ⋮ Duality versus dual flatness in quantum information geometry ⋮ Monotone norms and Finsler structures in noncommutative spaces ⋮ A geometry on the space of probabilities. II: Projective spaces and exponential families ⋮ The \(L^p\)-Fisher-Rao metric and Amari-Čencov \(\alpha\)-connections ⋮ Dual connections in nonparametric classical information geometry ⋮ On the monotonicity of scalar curvature in classical and quantum information geometry ⋮ On the characterisation of paired monotone metrics ⋮ DUAL GEOMETRY OF THE WIGNER–YANASE–DYSON INFORMATION CONTENT ⋮ Quantum Orlicz Spaces in Information Geometry ⋮ QUANTUM INFORMATION GEOMETRY AND NONCOMMUTATIVE L_p-SPACES ⋮ Amari-Chentsov connections and their geodesics on homogeneous spaces of diffeomorphism groups ⋮ ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY ⋮ A CHARACTERISATION OF WIGNER–YANASE SKEW INFORMATION AMONG STATISTICALLY MONOTONE METRICS

Cites Work

• \(L_ p\)-spaces for von Neumann algebra with reference to a faithful normal semifinite weight
• Applications of the complex interpolation method to a von Neumann algebra: non-commutative \(L^ p\)-spaces
• On the spatial theory of von Neumann algebras
• Les espaces \(L^ p\) d'une algebre de von Neumann definies par la derivee spatiale
• Notes on non-commutative integration
• \(\alpha\)-divergence of the non-commutative information geometry
• Generalized s-numbers of \(\tau\)-measurable operators
• A infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one
• On the Riemannian metric of \(\alpha\)-entropies of density matrices
• A non-commutative extension of abstract integration
• Connections on Non-Parametric Statistical Manifolds by Orlicz Space Geometry

This page was built for publication: CONNECTIONS ON STATISTICAL MANIFOLDS OF DENSITY OPERATORS BY GEOMETRY OF NONCOMMUTATIVE L^p-SPACES