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.