Journal of the Mathematical Society of Japan

A characterization of symmetric cones through pseudoinverse maps

Chifune KAI and Takaaki NOMURA

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Abstract

In this paper we characterize symmetric cones among homogeneous convex cones by the condition that the corresponding tube domains are mapped onto the dual tube domains under pseudoinverse maps with parameter. The condition also restricts the parameter to specific ones.

Article information

Source
J. Math. Soc. Japan, Volume 57, Number 1 (2005), 195-215.

Dates
First available in Project Euclid: 13 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1160745822

Digital Object Identifier
doi:10.2969/jmsj/1160745822

Mathematical Reviews number (MathSciNet)
MR2114729

Zentralblatt MATH identifier
1086.32021

Subjects
Primary: 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX] 43A85: Analysis on homogeneous spaces

Keywords
homogeneous cone symmetric cone clan pseudoinverse map tube domain

Citation

KAI, Chifune; NOMURA, Takaaki. A characterization of symmetric cones through pseudoinverse maps. J. Math. Soc. Japan 57 (2005), no. 1, 195--215. doi:10.2969/jmsj/1160745822. https://projecteuclid.org/euclid.jmsj/1160745822


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