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

 

Almost-everywhere discontinuity of the spectral radius


Author: Thomas J. Ransford
Journal: Proc. Amer. Math. Soc. 129 (2001), 749-751
MSC (2000): Primary 47A11
Published electronically: September 19, 2000
MathSciNet review: 1707001
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Abstract:

Let $\rho(T)$ denote the spectral radius of an operator $T$. We construct operators $S$ and $T$ on $\ell^2$ such that $\lambda\mapsto\rho(T-\lambda S)$ is discontinuous almost everywhere on the unit disk.


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Additional Information

Thomas J. Ransford
Affiliation: Département de Mathématiques et de Statistique, Université Laval, Québec, Québec, Canada G1K 7P4
Email: ransford@mat.ulaval.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05617-3
PII: S 0002-9939(00)05617-3
Received by editor(s): May 4, 1999
Published electronically: September 19, 2000
Additional Notes: The author’s research was supported by grants from NSERC (Canada) and the Fonds FCAR (Québec).
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society