Essential spectra through local spectral theory
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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.References
- Pietro Aiena, Riesz multipliers on commutative semisimple Banach algebras, Arch. Math. (Basel) 54 (1990), no. 3, 293–303. MR 1037620, DOI 10.1007/BF01188526
- Pietro Aiena and Kjeld B. Laursen, Multipliers with closed range on regular commutative Banach algebras, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1039–1048. MR 1185257, DOI 10.1090/S0002-9939-1994-1185257-1
- E Albrecht, J Eschmeier: Analytic functional models and local spectral theory (manuscript, 1987)
- E. Albrecht and R. D. Mehta, Some remarks on local spectral theory, J. Operator Theory 12 (1984), no. 2, 285–317. MR 757436
- Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0394282
- J Eschmeier, K B Laursen, M M Neumann: Multipliers with natural local spectra on commutative Banach algebras, J Functional Analysis, to appear.
- Domingo A. Herrero, On the essential spectra of quasisimilar operators, Canad. J. Math. 40 (1988), no. 6, 1436–1457. MR 990108, DOI 10.4153/CJM-1988-066-x
- Ronald Larsen, An introduction to the theory of multipliers, Die Grundlehren der mathematischen Wissenschaften, Band 175, Springer-Verlag, New York-Heidelberg, 1971. MR 0435738
- K B Laursen: Spectral subspaces and automatic continuity, Doctoral Dissertation, Copenhagen 1991.
- K. B. Laursen and M. Mbekhta, Closed range multipliers and generalized inverses, Studia Math. 107 (1993), no. 2, 127–135. MR 1244571
- Kjeld B. Laursen, Vivien G. Miller, and Michael M. Neumann, Local spectral properties of commutators, Proc. Edinburgh Math. Soc. (2) 38 (1995), no. 2, 313–329. MR 1335876, DOI 10.1017/S0013091500019106
- Kjeld B. Laursen and Michael M. Neumann, Local spectral properties of multipliers on Banach algebras, Arch. Math. (Basel) 58 (1992), no. 4, 368–375. MR 1152625, DOI 10.1007/BF01189927
- K. B. Laursen and M. M. Neumann, Asymptotic intertwining and spectral inclusions on Banach spaces, Czechoslovak Math. J. 43(118) (1993), no. 3, 483–497. MR 1249616
- Kjeld B. Laursen and Michael M. Neumann, Local spectral theory and spectral inclusions, Glasgow Math. J. 36 (1994), no. 3, 331–343. MR 1295508, DOI 10.1017/S0017089500030937
- K. B. Laursen and P. Vrbová, Some remarks on the surjectivity spectrum of linear operators, Czechoslovak Math. J. 39(114) (1989), no. 4, 730–739. MR 1018009
- Mostafa Mbekhta, Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), no. 2, 159–175 (French). MR 901662, DOI 10.1017/S0017089500006807
- Mostafa Mbekhta, Local spectrum and generalized spectrum, Proc. Amer. Math. Soc. 112 (1991), no. 2, 457–463. MR 1045142, DOI 10.1090/S0002-9939-1991-1045142-X
- T L Miller, V G Miller: Equality of essential spectra of quasisimilar operators with property $(\delta )$, Glasgow Math. J, to appear.
- V G Miller, M M Neumann: Local spectral theory for multipliers and convolution operators, in Algebraic methods in operator theory, Birkhäuser, Boston, 1994.
- 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.
- Ch. Schmoeger, Ein Spektralabbildungssatz, Arch. Math. (Basel) 55 (1990), no. 5, 484–489 (German). MR 1079997, DOI 10.1007/BF01190270
- Christoph Schmoeger, On isolated points of the spectrum of a bounded linear operator, Proc. Amer. Math. Soc. 117 (1993), no. 3, 715–719. MR 1111438, DOI 10.1090/S0002-9939-1993-1111438-8
- T. T. West, A Riesz-Schauder theorem for semi-Fredholm operators, Proc. Roy. Irish Acad. Sect. A 87 (1987), no. 2, 137–146. MR 941708
- Misha Zafran, On the spectra of multipliers, Pacific J. Math. 47 (1973), 609–626. MR 326309
Additional Information
- K. B. Laursen
- Affiliation: Matematisk Institut, Københavns Universitet, Universitetsparken 5, DK-2100 Køben- havn Ø, Denmark
- Email: laursen@math.ku.dk
- Received by editor(s): June 28, 1995
- Received by editor(s) in revised form: November 17, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1425-1434
- MSC (1991): Primary 47A10, 47A11, 47B40; Secondary 43A22, 46J10, 47A53
- DOI: https://doi.org/10.1090/S0002-9939-97-03852-5
- MathSciNet review: 1389525