On local irreducibility of the spectrum

Authors:
Constantin Costara and Thomas Ransford

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2779-2784

MSC (2000):
Primary 32Hxx; Secondary 15A18, 32A12, 47B49

DOI:
https://doi.org/10.1090/S0002-9939-07-08779-5

Published electronically:
February 6, 2007

MathSciNet review:
2317952

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the algebra of complex matrices, and for denote by and the spectrum and spectral radius of respectively. Let be a domain in containing 0, and let be a holomorphic map. We prove: (1) if for , then for ; (2) if for , then again for . Both results are special cases of theorems expressing the irreducibility of the spectrum near .

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Additional Information

**Constantin Costara**

Affiliation:
Faculty of Mathematics and Informatics, Ovidius University of Constanţa, Mamaia Boul. No. 124, 900527, Romania

Email:
cdcostara@univ-ovidius.ro

**Thomas Ransford**

Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4

Email:
ransford@mat.ulaval.ca

DOI:
https://doi.org/10.1090/S0002-9939-07-08779-5

Keywords:
Spectrum,
algebroid multifunction,
irreducible,
spectral radius,
preserver

Received by editor(s):
April 6, 2006

Received by editor(s) in revised form:
May 5, 2006

Published electronically:
February 6, 2007

Additional Notes:
The second author was supported by grants from NSERC and the Canada Research Chairs program

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2007
American Mathematical Society