Nonpositive curvature in p-Schatten class

Autor:	Cristian Marcelo Conde
Rok vydání:	2009
Předmět:	Matemáticas Applied Mathematics Mathematical analysis Uniform convexity Geodesic convexity Short geodesic Nonpositive curvature metric space Humanities CIENCIAS NATURALES Y EXACTAS p-Schatten class Analysis Matemática Pura Mathematics
Zdroj:	Journal of Mathematical Analysis and Applications. 356(2):664-673
ISSN:	0022-247X
DOI:	10.1016/j.jmaa.2009.03.036
Popis:	We study the geometry of the set p, with 1 < p < ∞, 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 dp and exposed several results about this metric space. The aim of this work is to prove that the space (p,dp) behaves in many senses like a nonpositive curvature metric space. Fil: Conde, Cristian Marcelo. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Databáze:	OpenAIRE
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