The index of triangular operator matrices
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- by K.-H. Förster and B. Nagy PDF
- Proc. Amer. Math. Soc. 128 (2000), 1167-1176 Request permission
Abstract:
For any triangular operator matrix acting in a direct sum of complex Banach spaces, the order of a pole of the resolvent (i.e. the index) is determined as a function of the coefficients in the Laurent series for all the (resolvents of the) operators on the diagonal and of the operators below the diagonal. This result is then applied to the case of certain nonnegative operators in Banach lattices. We show how simply these results imply the Rothblum Index Theorem (1975) for nonnegative matrices. Finally, examples for calculating the index are presented.References
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Additional Information
- K.-H. Förster
- Affiliation: Department of Mathematics, Technical University Berlin, Sekr. MA 6-4, Strasse des 17. Juni 135, D-10623 Berlin, Germany
- Email: foerster@math.tu-berlin.de
- B. Nagy
- Affiliation: Department of Analysis, Institute of Mathematics, Technical University Budapest, H-1521 Budapest, Hungary
- Email: bnagy@math.bme.hu
- Received by editor(s): October 10, 1997
- Received by editor(s) in revised form: June 17, 1998
- Published electronically: August 5, 1999
- Additional Notes: The second author was supported by the Hungarian NSF Grant (OTKA No. T-016925).
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1167-1176
- MSC (1991): Primary 47A10, 47B65; Secondary 15A18, 15A48
- DOI: https://doi.org/10.1090/S0002-9939-99-05341-1
- MathSciNet review: 1664366