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Borel reductibility and classification of von neumann algebras
(Association for Symbolic Logic, 2009-06)
We announce some new results regarding the classification problem for separable von Neumann algebras. Our results are obtained by applying the notion of Borel reducibility and Hjorth's theory of turbulence to the isomorphism ...
The classification problem for von Neumann factors
(Elsevier, 2008-12)
We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the ...
Metric geometry of partial isometries in a finite von Neumann algebra
(Universidad de San Andrés. Departamento de Matemáticas y Ciencias, 2006-06)
Geodesics of projections in von neumann algebras
(American Mathematical Society, 2021-07)
Let A be a von Neumann algebra and PA the manifold of projections in A. There is a natural linear connection in PA, which in the finite dimensional case coincides with the the Levi-Civita connection of the Grassmann manifold ...
Multiplicity theory of projections in abelian von neumann algebras
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 1988)
La teoría de multiplicidad espectral se generaliza para las proyecciones en un algebra conmutativa de von Neumann. La bien conocida descomposición de un álgebra de tipo I de von Neumann en una suma directa de álgebras de ...
Nonpositively curved metric in the positive cone of a finite von Neumann algebra
(Oxford University Press, 2006-08)
In this paper we study the metric geometry of the space Σ of positive invertible elements of a von Neumann algebra. A with a finite, normal and faithful tracial state T. The trace induces an incomplete Riemannian metric ...
The case of equality in Young's inequality for the s-numbers in semi-finite von Neumann algebras
(Theta Foundation, 2019-07)
For a semi-finite von Neumann algebra A, we study the case of equality in Young´s inequality of s-numbers for a pair of τ-measurable operators a,b, and we prove that equality is only possible if |a|^p=|b|^q. We also extend ...
Geometría diferencial de órbitas de estados en álgebras de operadoresDifferential geometry on state orbits in operator algebras
(Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires, 1996)