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http://dx.doi.org/10.1007/s00020-003-1313-1

has been cited by the following article:

• TITLE: Quasinilpotent Part of w-Hyponormal Operators

  AUTHORS: Mohammad Hussein Mohammad Rashid

  KEYWORDS: Aluthge Transformation, w-Hyponormal Operators, Polaroid Operators, Reguloid Operators, SVEP, Property β, Quasinilpotent Part

  JOURNAL NAME: Open Access Library Journal, Vol.1 No.6, September 19, 2014

  ABSTRACT: For a ω-hyponormal operator T acting on a separable complex Hilbert space , we prove that: 1) the quasi-nilpotent part H0 (T－λI) is equal to ker(T－λI); 2) T has Bishop’s property β; 3) if σω (T)={0} , then it is a compact normal operator; 4) If T is an al-gebraically ω-hyponormal operator, then it is polaroid and reguloid. Among other things, we prove that if Tn and Tn* are ω-hyponormal, then T is normal.