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http://dx.doi.org/10.4134/CKMS.2012.27.1.077

WEYL'S TYPE THEOREMS FOR ALGEBRAICALLY (p, k)-QUASIHYPONORMAL OPERATORS  

Rashid, Mohammad Hussein Mohammad (Department of Mathematics & Statistics Faculty of Science Mu'tah University)
Noorani, Mohd Salmi Mohd (School of mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia)
Publication Information
Communications of the Korean Mathematical Society / v.27, no.1, 2012 , pp. 77-95 More about this Journal
Abstract
For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.
Keywords
(p, k)-quasihyponormal; single valued extension property; Fred-holm theory; Browder's theory; spectrum;
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