Nonpositive curvature in p-Schatten class

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:356

Article

Conde, Cristian

关键词: p-Schatten class;    Nonpositive curvature metric space;    Geodesic convexity;    Short geodesic;    Uniform convexity;   

DOI  :  10.1016/j.jmaa.2009.03.036

来源: Elsevier

【 摘 要 】

We study the geometry of the set Delta p, with 1 < p < infinity, which consists of perturbations of the identity operator by p-Schatten class operators, which are positive and invertible as elements of B(H). These manifolds have natural and invariant Finsler structures. In [C. Conde, Geometric interpolation in p-Schatten class, J. Math. Anal. Appl. 340 (2008) 920-931], we introduced the metric d(p) and exposed several results about this metric space. The aim of this work is to prove that the space (Delta p, d(p)) behaves in many senses like a norpositive curvature metric space. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free