Let N be a statistical manifold of density operators, with respect to an n.s.f. trace tau on a semifinite von Neumann algebra M. If S-p is the unit sphere of the noncommutative space L-p(M, tau), using the noncommutative Amari embedding rho is an element of N --> rho(1/p) is an element of S-p, we define a noncommutative alpha-bundle-connection pair (F-alpha,del(alpha)), by the pullback technique. In the commutative case we show that it coincides with the construction of nonparametric Amari-Centsov alpha-connection made in Ref. 8 by Gibilisco and Pistone.
Gibilisco, P., & Isola, T. (1999). Connections on statistical manifolds of density operators by geometry of noncommutative L-p-spaces. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2(1), 169-178.
Tipologia: | Articolo su rivista |
Citazione: | Gibilisco, P., & Isola, T. (1999). Connections on statistical manifolds of density operators by geometry of noncommutative L-p-spaces. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2(1), 169-178. |
IF: | Con Impact Factor ISI |
Lingua: | English |
Settore Scientifico Disciplinare: | Settore MAT/06 - Probabilita' e Statistica Matematica |
Revisione (peer review): | Sì, ma tipo non specificato |
Tipo: | Articolo |
Rilevanza: | Rilevanza internazionale |
Stato di pubblicazione: | Pubblicato |
Data di pubblicazione: | 1999 |
Titolo: | Connections on statistical manifolds of density operators by geometry of noncommutative L-p-spaces |
Autori: | |
Autori: | Gibilisco, P; Isola, T |
Appare nelle tipologie: | 01 - Articolo su rivista |
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