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arXiv · 2507.01847

On $C$-Symmetric and $C$-Self-adjoint Unbounded Operators on Hilbert Space

Yury Arlinskii·Konrad Schmüdgen
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Abstract

Let $C$ be a conjugation on a Hilbert space $\mathcal{H}$. A densely defined linear operator $A$ on $\mathcal{H}$ is called $C$-symmetric if $CAC\subseteq A^*$ and $C$-self-adjoint if $CAC=A^*$. Our main results describe all $C$-self-adjoint extensions of $A$ on $\mathcal{H}$. Further, we prove a $C$-self-adjointness criterion based on quasi-analytic vectors and we characterize $C$-self-adjoint operators in terms of their polar decompositions.

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Yury Arlinskii, Konrad Schmüdgen. 2025-07-02. On $C$-Symmetric and $C$-Self-adjoint Unbounded Operators on Hilbert Space. https://arxiv.org/abs/2507.01847

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