@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 <i>T</i> to satisfy the generalized &#945;-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 &#963;(<i>T</i>). As applications, we show that if <i>T</i><SUP>*</SUP> is algebraically &#969;<i>F</i>(<i>p</i>,<i>r</i>,<i>q</i>) for each <i>p</i>,<i>r</i>>0 and q&#8805;1, or if <i>T</i><SUP>*</SUP> is algebraically quasi-class <i>A</i>, then the generalized &#945;-WeylĄ¯s theorem hold for <i>f</i>(<i>T</i>), where <i>f</i>&#8712;<i>Hol</i>(&#963;(<i>T</i>)), the space of functions analytic on an open neighborhoods of &#963;(<i>T</i>).},
doi={10.12691/tjant-4-5-5}
publisher={Science and Education Publishing}
}