Title : ( Solutions to the operator equation f (XX*) = g(X*X) )
Authors: Rasoul Eskandari , Mohammad Sal Moslehian , Ali Talebi ,
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Abstract
The characterization of special operators (or matrices), such as normal and self- adjoint (Hermitian) ones, through operator (or matrix) equations has been a topic of signif- icant interest for a long time. In this paper, we explore equations involving products of an operator X and its adjoint X ∗ . We provide new characterizations of normal and Hermitian matrices using general matrix equations. We then extend and improve these results to oper- ators on Hilbert spaces of any dimension. Moreover, we establish further characterizations of normal and self-adjoint operators (and matrices) based on our findings.
Keywords
, Matrix equation, Normal matrix, Polar decomposition, Compact normal operator
@article{paperid:1107171,
author = {رسول اسکندری and Sal Moslehian, Mohammad and Ali Talebi, },
title = {Solutions to the operator equation f (XX*) = g(X*X)},
journal = {Aequationes Mathematicae},
year = {2026},
volume = {40},
number = {2},
month = {April},
issn = {0001-9054},
pages = {1--9},
numpages = {8},
keywords = {Matrix equation; Normal matrix; Polar decomposition; Compact normal operator},
}
%0 Journal Article
%T Solutions to the operator equation f (XX*) = g(X*X)
%A رسول اسکندری
%A Sal Moslehian, Mohammad
%A Ali Talebi,
%J Aequationes Mathematicae
%@ 0001-9054
%D 2026
