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Laursen, K. B.

Essential spectra through local spectral theory. (English) Zbl 0871.47003

Proc. Am. Math. Soc. 125, No. 5, 1425-1434 (1997).
Summary: 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.

Cited in 4 Documents

MSC:

47A10 Spectrum, resolvent
47A53 (Semi-) Fredholm operators; index theories
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
46J10 Banach algebras of continuous functions, function algebras
47A11 Local spectral properties of linear operators
47B40 Spectral operators, decomposable operators, well-bounded operators, etc.

Keywords:

local spectral theory; semi-Fredholm spectrum; weak intertwining relations; decomposable operators; multipliers on commutative semisimple Banach algebras
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References:

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