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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Discontinuity of the Lempert function of the spectral ball


Authors: Pascal J. Thomas and Nguyen Van Trao
Journal: Proc. Amer. Math. Soc. 138 (2010), 2403-2412
MSC (2010): Primary 32F45; Secondary 32U35
Published electronically: February 24, 2010
MathSciNet review: 2607870
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Abstract: We give some further criteria for continuity or discontinuity of the Lempert function of the spectral ball $ \Omega_n$, with respect to one or both of its arguments, in terms of cyclicity of the matrices involved.


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Pascal J. Thomas
Affiliation: Institut de Mathématiques de Toulouse, Université de Toulouse, UPS, INSA, UT1, UTM, F-31062 Toulouse, France
Email: pthomas@math.univ-toulouse.fr

Nguyen Van Trao
Affiliation: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy str - Cau Giay, Hanoi, Vietnam
Email: ngvtrao@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10269-X
PII: S 0002-9939(10)10269-X
Received by editor(s): March 6, 2009
Received by editor(s) in revised form: September 5, 2009
Published electronically: February 24, 2010
Additional Notes: The initial version of this paper was written during the second author’s stay at the Paul Sabatier University, Toulouse, with the help of the Formath Vietnam program.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.