CONNECTIONS ON STATISTICAL MANIFOLDS OF DENSITY OPERATORS BY GEOMETRY OF NONCOMMUTATIVE Lp-SPACES
Authors:
- 1 March 1999
- journal article
- review article
- Published by World Scientific Pub Co Pte Ltd in Infinite Dimensional Analysis, Quantum Probability and Related Topics
- Vol. 02 (01) , 169-178
Abstract
Let [Formula: see text] be a statistical manifold of density operators, with respect to an n.s.f. trace τ on a semifinite von Neumann algebra M. If Sp is the unit sphere of the noncommutative space Lp(M, τ), using the noncommutative Amari embedding [Formula: see text], we define a noncommutative α-bundle-connection pair (ℱα, ∇α), by the pullback technique. In the commutative case we show that it coincides with the construction of nonparametric Amari–Čentsov α-connection made in Ref. 8 by Gibilisco and Pistone.Keywords
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