Antilinar Normal Operators on Hilbert Space

Abstract

An operator $A$ on a complex Hilbert space $\Hh$ is called antilinear if $A(x+y)=Ax+Ay$ and $A(λx)=\ovλ Ax$ for $x,y\in \cD(A)$ and $λ\in \dC$. We investigate some classes of densely defined antilinear unbounded operators, especially antilinear normal operators. We give various characterizations of antilinear normal operators and study a class of such operators in detail. Our main result is a structure theorem for unbounded antilinear normal operators.