On linear operators for which TTD is normal | Zendy

R. Yousefi | Zendy; М. Дана | Zendy

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On 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.

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