%0 Journal Article
%T Quasinilpotent Part of w-Hyponormal Operators
%A Mohammad Rashid
%J Open Access Library Journal
%V 1
%N 6
%P 1-15
%@ 2333-9721
%D 2014
%I Open Access Library
%R 10.4236/oalib.1100548
%X For a w-hyponormal operator T acting on a separable complex Hilbert
space H, we prove that: 1) the quasi-nilpotent part Ho(T - ¦ËI ) is equal to Ker(T- ¦ËI); 2) T has Bishop¡¯s property<i>¦Â</i>; 3) if ¦Òw (T)={0}, then it is a compact normal operator; 4) If T is
an algebraically w-hyponormal operator, then it is polaroid and reguloid. Among
other things, we prove that ifTn and Tn* are w-hyponormal, then T is normal.
%K Aluthge Transformation
%K w-Hyponormal Operators
%K Polaroid Operators
%K Reguloid Operators
%K SVEP
%K Property ¦Â
%K Quasinilpotent Part
%U http://www.oalib.com/paper/3064412