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...
Збережено в:
| Дата: | 2025 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2025
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8685 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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 |