Spaces of nonpositive curvature arising from a finite algebra

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:368

Article

Conde, Cristian^1,2  Larotonda, Gabriel^1,2 

[1] Univ Nacl Gen Sarmiento, Inst Ciencias, Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, Inst Argentino Matemat Alberto Calderon, RA-1033 Buenos Aires, DF, Argentina

关键词: Geodesic convexity;    Noncommutative measure spaces;    Positive cone;    Short geodesic;    Uniform convexity;   

DOI  :  10.1016/j.jmaa.2010.03.029

来源: Elsevier

【 摘 要 】

In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are modelled on a finite von Neumann algebra, and the metrics introduced arise from the trace of the algebra. In spite of the noncompleteness of these manifolds, their geometry can be studied from the view-point of metric geometry, and several techniques derived from the functional analysis are applied to gain insight on their geodesic structure. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free