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Essential spectra
through local spectral theory

Author: K. B. Laursen
Journal: Proc. Amer. Math. Soc. 125 (1997), 1425-1434
MSC (1991): Primary 47A10, 47A11, 47B40; Secondary 43A22, 46J10, 47A53
MathSciNet review: 1389525
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Abstract: Based on a nice observation of Eschmeier, this is a study of the use of local spectral theory in investigations of the semi-Fredholm spectrum of a continuous linear operator. We also examine the retention of the semi-Fredholm spectrum under weak intertwining relations; it is shown, inter alias, that if two decomposable operators are intertwined asymptotically by a quasi-affinity then they have identical semi-Fredholm spectra. The results are applied to multipliers on commutative semisimple Banach algebras.

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  • 1. P Aiena: Riesz multipliers on commutative semisimple Banach algebras, Arch.Math. 54 (1990), 293-303. MR 91e:46064
  • 2. P Aiena, K B Laursen: Multipliers with closed range on regular commutative Banach algebras, Proc.Amer. Math.Soc. 121 (1994), 1039-1048. MR 94j:46051
  • 3. E Albrecht, J Eschmeier: Analytic functional models and local spectral theory (manuscript, 1987)
  • 4. E Albrecht, R D Mehta: Some remarks on local spectral theory, J. Operator Theory, 12 (1984), no. 2, 285-317. MR 85m:47031
  • 5. I Colojoara, C Foias: Theory of generalized spectral operators, Gordon and Breach, New York 1968. MR 52:15085
  • 6. J Eschmeier, K B Laursen, M M Neumann: Multipliers with natural local spectra on commutative Banach algebras, J Functional Analysis, to appear.
  • 7. D A Herrero: On the essential spectra of quasi-similar operators, Can. J Math. 40 (1988), 1436-1457. MR 90b:47006
  • 8. R Larsen: An introduction to the theory of multipliers, Springer-Verlag, New York 1971. MR 55:8695
  • 9. K B Laursen: Spectral subspaces and automatic continuity, Doctoral Dissertation, Copenhagen 1991.
  • 10. K B Laursen, M Mbekhta: Closed range multipliers and generalized inverses, Studia Math. 107 (2) (1993), 127-135. MR 94i:47052
  • 11. K B Laursen, V G Miller, M M Neumann: Local spectral properties of commutators, Proc. Edinburgh Math. Soc., 38 (1995), 313-329. MR 96f:47066
  • 12. K B Laursen, M M Neumann: Local spectral properties of multipliers on Banach algebras, Arch. Math. 58 (1992), 368-375. MR 93e:46058
  • 13. K B Laursen, M M Neumann: Asymptotic intertwining and spectral inclusions on Banach spaces, Czechoslovak Math. J 43 (118) (1993), 483-497. MR 94k:47007
  • 14. K B Laursen, M M Neumann: Local spectral theory and spectral inclusions, Glasgow Math. J 36 (1994), 331-343. MR 95k:47002
  • 15. K B Laursen, P Vrbova: Some remarks on the surjectivity spectrum of linear operators, Czechoslovak Math. J 39 (114) (1989), 730-739. MR 90m:47010
  • 16. M Mbekhta: Generalisations de la decomposition de Kato aux opérateurs paranormaux et spectraux, Glasgow Math. J 29 (1987), 159-175. MR 88i:47010
  • 17. M Mbekhta: Local spectrum and generalized spectrum , Proc. Amer. Math. Soc. 112 (1991), 457-463. MR 91i:47004
  • 18. T L Miller, V G Miller: Equality of essential spectra of quasisimilar operators with property $(\delta )$, Glasgow Math. J, to appear. CMP 96:08
  • 19. V G Miller, M M Neumann: Local spectral theory for multipliers and convolution operators, in Algebraic methods in operator theory, Birkhäuser, Boston, 1994.
  • 20. M M Neumann: Local spectral theory for operators on Banach space and applications to convolution operators on group algebras, in Seminar Notes in Functional Analysis and PDEs 1993/94, Department of Mathematics, Louisiana State University, Baton Rouge, LA, 1994.
  • 21. C Schmoeger: Ein Spektralabbildungssatz, Arch. Math. 55 (1990), 484-489. MR 92h:47007
  • 22. C Schmoeger: On isolated points of the spectrum of a bounded linear operator, Proc. Amer.Math. Soc. 117 (1993), 715-719. MR 93d:47007
  • 23. T T West: A Riesz-Schauder theorem for semi-Fredholm operators, Proc. Royal Irish Acad. 87A (1987), 137-146. MR 89i:47020
  • 24. M Zafran: On the spectra of multipliers, Pac. J Math. 47 (1973), 609-626.

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Additional Information

K. B. Laursen
Affiliation: Matematisk Institut, Københavns Universitet, Universitetsparken 5, DK-2100 Køben- havn Ø, Denmark

Received by editor(s): June 28, 1995
Received by editor(s) in revised form: November 17, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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