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Browder's theorems andspectral continuity

Published online by Cambridge University Press:  13 November 2000

Slaviša V. Djordjević  and
Young Min Han
Slaviša V. Djordjević
Affiliation:
University of Nisˇ, Faculty of Philosophy, Department of Mathematics, Ćirila and Metodija 2, 18000 Niš, Yugoslavia. E-mail: slavdj@archimed.filfak.ni.ac.yu
Young Min Han
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea. E-mail: ymhan@math.skku.ac.kr
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Abstract

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Let X be a complex infinite dimensional Banach space. We use σ_a(T) andσ_{ea}(T) , respectively, to denote the approximate point spectrum and the essential approximate point spectrum of a bounded operator T onX . Also, \pi _a(T) denotes the set <$>{\rm{iso} σ_a(T)\backslash σ_{ea}(T)}<$>. An operator T onX obeys the a-Browder's theorem provided that<$>σ_{ea}(T) =σ_a(T\,)\backslash π_a(T)<$> . We investigate connections between the Browder's theorems, the spectral mapping theorem and spectral continuity.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 3 , September 2000 , pp. 479 - 486
Copyright
2000 Glasgow Mathematical Journal Trust