@article{tjant2016455,
author={RASHID, M. H. M.},
title={Generalized α-Browder's and Generalized α-Weyl's Theorems for Banach Space},
journal={Turkish Journal of Analysis and Number Theory},
volume={4},
number={5},
pages={146--154},
year={2016},
url={http://pubs.sciepub.com/tjant/4/5/5},
issn={2333-1232},
abstract={In this paper, we give necessary and sufficient conditions for a Banach space *T* to satisfy the generalized α-BrowderĄ¯s theorem. We also prove that the spectral mapping theorem holds for the left Drazin invertible and for analytic functions on a neighborhood of σ(*T*). As applications, we show that if *T*^{*} is algebraically ω*F*(*p*,*r*,*q*) for each *p*,*r*>0 and q≥1, or if *T*^{*} is algebraically quasi-class *A*, then the generalized α-WeylĄ¯s theorem hold for *f*(*T*), where *f*∈*Hol*(σ(*T*)), the space of functions analytic on an open neighborhoods of σ(*T*).},
doi={10.12691/tjant-4-5-5}
publisher={Science and Education Publishing}
}