Author(s)

Mohammad Hussein Mohammad Rashid

Department of Mathematics & Statistics, Faculty of Science, Mu’tah University, Mu’tah, Jordan.

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 σ_ω (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 T^n* are ω-hyponormal, then T is normal.

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

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