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.

Connections on statistical manifolds of density operators by geometry of noncommutative L-p-spaces

GIBILISCO, PAOLO;ISOLA, TOMMASO
1999

Abstract

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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/06 - Probabilita' e Statistica Matematica
English
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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.
Gibilisco, P; Isola, T
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/49736
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