$C$--normal operators

TL;DR

This paper introduces the class of $C$--normal operators, expanding beyond $C$-symmetric and normal operators, with properties and finite-dimensional characterizations related to conjugate normal matrices.

Contribution

It defines and explores properties of $C$--normal operators, providing new characterizations especially in finite-dimensional spaces.

Findings

$C$--normal operators form a larger class than $C$-symmetric operators.

Finite-dimensional characterizations relate $C$--normal operators to conjugate normal matrices.

Basic properties of $C$--normal operators are established.

Abstract

A new class of operators, larger than $C$-symmetric operators and different than normal one, named $C$--normal operators is introduced. Basic properties are given. Characterizations of this operators in finite dimensional spaces using a relation with conjugate normal matrices are presented.