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<p>The regular subspaces of a Kreĭn space have well-known properties analogous to the closed subspaces of a Hilbert space. A boundedness condition on sums of projection operators extends this analogy to a natural notion of infinite orthogonal direct sums. The boundedness condition is shown to have several equivalent forms and consequences for Cartesian products. Moore-Smith convergence and a theorem of T.&#xa0;H. Hildebrandt play key roles in the formulation of results and proofs.</p>

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Rearrangement Invariant Orthogonal Sums in Kreĭn Spaces. I

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月31日

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  • James Rovnyak

摘要

The regular subspaces of a Kreĭn space have well-known properties analogous to the closed subspaces of a Hilbert space. A boundedness condition on sums of projection operators extends this analogy to a natural notion of infinite orthogonal direct sums. The boundedness condition is shown to have several equivalent forms and consequences for Cartesian products. Moore-Smith convergence and a theorem of T. H. Hildebrandt play key roles in the formulation of results and proofs.