Quasinilpotent Part of w-Hyponormal Operators


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.

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Rashid, M. (2014) Quasinilpotent Part of w-Hyponormal Operators. Open Access Library Journal, 1, 1-15. doi: 10.4236/oalib.1100548.

Conflicts of Interest

The authors declare no conflicts of interest.


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