Journal of the Mathematical Society of Japan

A characterization of symmetric cones through pseudoinverse maps

Chifune KAI and Takaaki NOMURA

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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.

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

First available in Project Euclid: 13 October 2006

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Zentralblatt MATH identifier

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

homogeneous cone symmetric cone clan pseudoinverse map tube domain


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.

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