Open AccessOn linear operators for which TTD is normal
Author(s) -
R. Yousefi,
М. Дана
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1909695y
Subject(s) - mathematics , invertible matrix , skew , operator (biology) , operator matrix , pure mathematics , commutative property , normal matrix , matrix (chemical analysis) , discrete mathematics , algebra over a field , eigenvalues and eigenvectors , computer science , telecommunications , biochemistry , chemistry , physics , materials science , repressor , quantum mechanics , transcription factor , composite material , gene
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.