Affiliation:
1. Faculty of Mathematics, University of Kurdistan, Sanandaj, Islamic Republic of Iran
Abstract
A Drazin invertible operator T ? B(H) is called skew D-quasi-normal operator
if T* and TTD commute or equivalently TTD is normal. In this paper, firstly
we give a list of conditions on an operator T; each of which is equivalent
to T being skew D-quasi-normal. Furthermore, we obtain the matrix
representation of these operators. We also develop some basic properties of
such operators. Secondly we extend the Kaplansky theorem and the
Fuglede-Putnam commutativity theorem for normal operators to skew
D-quasi-normal matrices.
Publisher
National Library of Serbia