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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 $f{\in}Hol({\sigma}T))$.
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참고문헌 (31)
참고문헌 신청
A.-H. Kim / 1999 / Weyl's theorem for isoloid and reguloid operators / Commun. Korean Math. Soc 14 (1) : 179 ~ 188
B. P. Dugga / 2004 / Generalised Weyl's theorem for a class of operators satisfying a norm condition / Math. Proc. R. Ir. Acad 104 (1) : 75 ~ 81
B. P. Duggal / 2004 / Generalized Weyl's theorem for a class of operators satisfying a norm condition / Proc. Roy. Irish Acad. Sect. A 104 (1) : 271 ~ 277
H. R. Dowson / 1978 / Spectral Theory of Linear Operators / Academic Press
I. H. Kim / 2004 / On (p, k)-quasihyponormal operators / Math. Inequal. Appl 7 (4) : 629 ~ 638
B. P. Dugga / 2004 / Generalised Weyl's theorem for a class of operators satisfying a norm condition / Math. Proc. R. Ir. Acad 104 (1) : 75 ~ 81
B. P. Duggal / 2004 / Generalized Weyl's theorem for a class of operators satisfying a norm condition / Proc. Roy. Irish Acad. Sect. A 104 (1) : 271 ~ 277
H. R. Dowson / 1978 / Spectral Theory of Linear Operators / Academic Press
I. H. Kim / 2004 / On (p, k)-quasihyponormal operators / Math. Inequal. Appl 7 (4) : 629 ~ 638
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