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<p>The <i>G</i>-construction allows us to obtain a certain system of subspaces by using an abstract Gram operator. Any system of subspaces is unitarily equivalent to a system constructed by using this method. We propose another construction of a system of subspaces with the same property, provide criteria for the unitary equivalence of a pair of systems of subspaces in terms of the corresponding Gram operators, and study the problem of irreducibility of a system of subspaces in terms of the corresponding Gram operator. In addition, we provide an example illustrating the application of the obtained results to the investigation of a certain class of systems of subspaces.</p>

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On Some Properties of the Gram Operator

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Oleksandr Strilets

摘要

The G-construction allows us to obtain a certain system of subspaces by using an abstract Gram operator. Any system of subspaces is unitarily equivalent to a system constructed by using this method. We propose another construction of a system of subspaces with the same property, provide criteria for the unitary equivalence of a pair of systems of subspaces in terms of the corresponding Gram operators, and study the problem of irreducibility of a system of subspaces in terms of the corresponding Gram operator. In addition, we provide an example illustrating the application of the obtained results to the investigation of a certain class of systems of subspaces.