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<p>Given a conjugation (involution) <i>C</i> on a Hilbert space, <i>C</i>-self-adjoint contractive extensions of a non-densely defined <i>C</i>-symmetric contraction are studied and parameterizations of all such extensions are obtained. As an application, a proof of an announced result of Glazman [<CitationRef CitationID="CR15">15</CitationRef>] on the existence of maximal dissipative <i>C</i>-self-adjoint extensions of a densely defined <i>C</i>-symmetric dissipative operator is given.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Yury Arlinskiĭ,
  • Konrad Schmüdgen

摘要

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 [15] on the existence of maximal dissipative C-self-adjoint extensions of a densely defined C-symmetric dissipative operator is given.