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arXiv · 2606.05943

Antilinar Normal Operators on Hilbert Space

Konrad Schmüdgen
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Abstract

An operator $A$ on a complex Hilbert space $\Hh$ is called antilinear if $A(x+y)=Ax+Ay$ and $A(\lambda x)=\ov{\lambda} Ax$ for $x,y\in \cD(A)$ and $\lambda\in \dC$. 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.

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Konrad Schmüdgen. 2026-06-04. Antilinar Normal Operators on Hilbert Space. https://arxiv.org/abs/2606.05943

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