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<p>The goal of this article is to study the properties of the quasi-projection pair (<i>P</i>,&#xa0;<i>Q</i>) with projection <i>P</i> and idempotent <i>Q</i> defined on a Hilbert space. We present characterizations of quasi-projection pairs in terms of spectrum, Hilbert space decomposition and norm inequalities. To this end a matrix representation of a quasi-projection pair with respect to their ranges is described.</p>

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Some Characterizations of the Quasi-Projection Pair

  • 期刊论文

  • 发表日期：

    2025年3月14日

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  • Xiaohui Li,
  • Chunyuan Deng,
  • Xindi Deng

摘要

The goal of this article is to study the properties of the quasi-projection pair (P, Q) with projection P and idempotent Q defined on a Hilbert space. We present characterizations of quasi-projection pairs in terms of spectrum, Hilbert space decomposition and norm inequalities. To this end a matrix representation of a quasi-projection pair with respect to their ranges is described.