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ON THE EQUIVALENCE OF BROWDER'S AND GENERALIZED BROWDER'S THEOREM

Published online by Cambridge University Press:  24 March 2006

M. AMOUCH  and
H. ZGUITTI
M. AMOUCH
Affiliation:
Department of Mathematics, Faculty of science, Semlalia, B.O: 2390 Marrakesh, Morocco e-mail: [email protected]
H. ZGUITTI
Affiliation:
Department of Mathematics, Faculty of science, of Rabat, B.O: 1014 Rabat, Morocco. e-mail: [email protected]
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Abstract

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In this note we answer two question posed by Berkani and Koliha [Acta Sci. Math.69 (2003), 359–376]. We show that generalized Browder's (resp. generalized $a$-Browder's) theorem holds for a Banach space operator if and only if Browder's (resp. $a$-Browder's) theorem does. We also give condition under which generalized Weyl's (resp. generalized $a$-Weyl's) theorem is equivalent to Weyl's (resp. $a$-Weyl's) theorem.

Keywords

Primary 47A53Secondary 47A1047A11
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 1 , January 2006 , pp. 179 - 185
Copyright
2006 Glasgow Mathematical Journal Trust