Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on meromorphic operators

Author: Christoph Schmoeger
Journal: Proc. Amer. Math. Soc. 133 (2005), 511-518
MSC (2000): Primary 47A10, 47A11
Published electronically: August 4, 2004
MathSciNet review: 2093075
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ be a complex Banach space and $T$ a bounded linear operator on $X$. $T$ is called meromorphic if the spectrum $\sigma(T)$ of $T$is a countable set, with $0$ the only possible point of accumulation, such that all the nonzero points of $\sigma(T)$ are poles of $(\lambda I-T)^{-1}$. By means of the analytical core $K(T)$ we give a spectral theory of meromorphic operators. Our results are a generalization of some results obtained by Gong and Wang (2003).

References [Enhancements On Off] (What's this?)

  • 1. W. Bouamama, Opérateurs de Riesz dont le coeur analytique est fermé, Stud. Math., to appear.
  • 2. I. Colojoara, C. Foias, Theory of generalized spectral operators, Gordon and Breach, New York, 1968. MR 52:15085
  • 3. J. K. Finch, The single-valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61-69. MR 51:11181
  • 4. H. Heuser, Funktionalanalysis, 2nd ed., Teubner, Stuttgart, 1986. MR 90m:46001
  • 5. M. Mbekhta, Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), 159-175. MR 88i:47010
  • 6. M. Mbekhta, Sur la théorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 110 (1990), 621-631. MR 91b:47004
  • 7. W. Gong, L. Wang, Mbekhta's subspaces and a spectral theory of compact operators, Proc. Amer. Math. Soc. 131 (2003), 578-592. MR 2003g:47004
  • 8. C. Schmoeger, On isolated points of the spectrum of a bounded linear operator, Proc. Amer. Math. Soc. 117 (1993), 715-719. MR 93d:47007

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A10, 47A11

Retrieve articles in all journals with MSC (2000): 47A10, 47A11

Additional Information

Christoph Schmoeger
Affiliation: Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Keywords: Meromorphic operators, analytical core
Received by editor(s): August 15, 2003
Received by editor(s) in revised form: October 20, 2003
Published electronically: August 4, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society