On some properties of the Gram operator

UDC 512.552.4 The $G$-construction allows us to obtain a system of subspaces 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 c...

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Datum:2025
Hauptverfasser: Strilets, O., Стрілець, Олександр
Format: Artikel
Sprache:Ukrainisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2025
Online Zugang:https://umj.imath.kiev.ua/index.php/umj/article/view/8685
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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Zusammenfassung:UDC 512.552.4 The $G$-construction allows us to obtain a system of subspaces 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 how the obtained results apply to the study of a certain class of the systems of subspaces.
DOI:10.3842/umzh.v77i3.8685