Open AccessPolar decomposition and characterization of binormal operators
Author(s) -
Karizaki Mehdi Mohammadzadeh
Publication year - 2020
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/fil2003013m
Subject(s) - mathematics , polar decomposition , operator (biology) , inverse , linear map , moore–penrose pseudoinverse , transformation (genetics) , pure mathematics , characterization (materials science) , product (mathematics) , representation (politics) , polar , range (aeronautics) , algebra over a field , geometry , biochemistry , chemistry , physics , materials science , repressor , astronomy , politics , political science , transcription factor , law , composite material , gene , nanotechnology
We illustrate the matrix representation of the closed range operator that enables us to determine the polar decomposition with respect to the orthogonal complemented submodules. This result proves that the reverse order law for the Moore-Penrose inverse of operators holds. Also, it is given some new characterizations of the binormal operators via the generalized Aluthge transformation. New characterizations of the binormal operators enable us to obtain equivalent conditions when the inner product of the binormal operator with its generalized Aluthge transformation is positive in the general setting of adjointable operators on Hilbert C*-modules.