$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions

Yury Arlinskii; Konrad Schmüdgen

$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions

Functional Analysis 2025-08-05 v2

Authors: Yury Arlinskii , Konrad Schmüdgen

Abstract

Given a conjugation (involution) $C$ on a Hilbert space, $C$ -self-adjoint contractive extensions of a non-densely defined $C$ -symmetric contraction are studied and parameterizations of all such extensions are obtained. As an application, a proof of an announced result of Glazman \cite{Glazman1} on the existence of maximal dissipative $C$ -self-adjoint extensions of a densely defined $C$ -symmetric dissipative operator is given.

Keywords

$C$-self-adjoint extension conjugation contraction operator dissipative operator parameterization

Cite

@article{arxiv.2506.14357,
  title  = {$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions},
  author = {Yury Arlinskii and Konrad Schmüdgen},
  journal= {arXiv preprint arXiv:2506.14357},
  year   = {2025}
}

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21 pages

$C$-self-adjoint contractive extensions of $C$-symmetric non-densely defined contractions

Abstract

Keywords

Cite

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