Glasgow Mathematical Journal

Browder's theorems and spectral continuity

Slaviša V. Djordjevic a1 and Young Min Han a2
a1 University of Nis[caron], Faculty of Philosophy, Department of Mathematics, Cirila and Metodija 2, 18000 Niš, Yugoslavia. E-mail:
a2 Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea. E-mail:


Let X be a complex infinite dimensional Banach space. We use &sigma;_a(T) and&sigma;_{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 <$>{\rm{iso} &sigma;_a(T)\backslash &sigma;_{ea}(T)}<$>. An operator T onX obeys the a-Browder's theorem provided that<$>&sigma;_{ea}(T) =&sigma;_a(T\,)\backslash &pi;_a(T)<$> . We investigate connections between the Browder's theorems, the spectral mapping theorem and spectral continuity.

(Received February 10 1999)