An approach to the spectrum structure of Dirac operators by the local-compactness method

Authors:
Tadashi Ikuta and Kazuhisa Shima

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1471-1479

MSC (1991):
Primary 34L05, 34L40

Published electronically:
September 20, 2002

MathSciNet review:
1949877

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Abstract: The purpose of this paper is to investigate the spectra of the Dirac operator . The local compactness of is shown under some assumption on . This method enables us to prove that if as , then and to give a significant sufficient condition that or has a purely discrete spectrum.

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Additional Information

**Tadashi Ikuta**

Affiliation:
Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo, Noda, Chiba 278-8510, Japan

Email:
ikuta_tadashi@ma.noda.tus.ac.jp

**Kazuhisa Shima**

Affiliation:
Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo, Noda, Chiba 278-8510, Japan

Email:
shima@rs.noda.tus.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-02-06661-3

Keywords:
Locally compact operator,
Dirac operator,
essential spectrum,
discrete spectrum

Received by editor(s):
November 29, 2000

Received by editor(s) in revised form:
March 29, 2001, and December 11, 2001

Published electronically:
September 20, 2002

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2002
American Mathematical Society