Proceedings of the American Mathematical Society

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



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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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