대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권1호
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  • Pages.77-95
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  • 2012
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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WEYL'S TYPE THEOREMS FOR ALGEBRAICALLY (p, k)-QUASIHYPONORMAL OPERATORS

  • 투고 : 2009.06.22
  • 발행 : 2012.01.31
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초록

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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피인용 문헌

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