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<p>We extend the study of normal projections in Krein spaces to the unbounded case. We characterize both weakly normal and normal projections, and prove that every normal projection admits a decomposition as the sum of a selfadjoint projection and a closed projection with neutral range. We show that every closed subspace <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation> is the range of a (possibly unbounded) normal projection and parametrize the set of normal projections onto <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">S</mi> </math></EquationSource> </InlineEquation> using the notion of normal companions.</p>

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Normal Projections in Krein Spaces II

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Maximiliano Contino,
  • Alejandra Maestripieri,
  • Francisco Martínez Pería

摘要

We extend the study of normal projections in Krein spaces to the unbounded case. We characterize both weakly normal and normal projections, and prove that every normal projection admits a decomposition as the sum of a selfadjoint projection and a closed projection with neutral range. We show that every closed subspace \(\mathcal {S}\) S is the range of a (possibly unbounded) normal projection and parametrize the set of normal projections onto \(\mathcal {S}\) S using the notion of normal companions.