Affine connections, duality and divergences for a von Neumann algebra

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dc.creatorJencova, Anna
dc.date2003-11-05
dc.date.accessioned2026-07-07T04:30:42Z
dc.date.available2026-07-07T04:30:42Z
dc.descriptionOn the predual of a von Neumann algebra, we define a differentiable manifold structure and affine connections by embeddings into non-commutative L_p-spaces. Using the geometry of uniformly convex Banach spaces and duality of the L_p and L_q spaces for 1/p+1/q=1, we show that we can introduce the α-divergence, for αin (-1,1), in a similar manner as Amari in the classical case. If restricted to the positive cone, the α-divergence belongs to the class of quasi-entropies, defined by Petz.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0311004
dc.identifierhttp://arxiv.org/abs/math-ph/0311004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57553
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.titleAffine connections, duality and divergences for a von Neumann algebra
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