| Форма представления | Статьи в зарубежных журналах и сборниках |
| Год публикации | 2025 |
| Язык | английский |
|
Бикчентаев Айрат Мидхатович, автор
|
|
Moslehian Mohammad Sal , автор
Moslehian Mohammad Sal , автор
|
| Библиографическое описание на языке оригинала |
Airat M. Bikchentaev, Mohammad Sal Moslehian, On pairs of projections //
Positivity, 2025, V. 29, no. 4. Paper No. 47. -- 13 pp. |
| Аннотация |
Two projections P and Q on a Hilbert space H are called acute if PQ < 1. We utilize the von Neumann alternating projection theorem to prove that if P and Q are acute, then P ∧ Q = 0. Conversely, if P ∧ Q = 0 and PQ is a compact operator, then P and Q are acute. An example is presented to show that the assumption of compactness is necessary. Let M be a von Neumann algebra, M pr be the lattice of all projections in M, and P, Q ∈ M pr . A pair (P, Q) is called modular in M pr if (R ∨ P) ∧ Q = (R ∧ Q) ∨ (P ∧ Q) for every R ∈ M pr with R ≤ Q. We present several characterizations of modular pairs of projections in a von Neumann algebra. In particular, for a factor M of type I or III, we investigate certain modularity conditions. |
| Ключевые слова |
Acute projections, modular projections, isoclinic projections |
| Название журнала |
POSITIVITY
|
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=315890 |
| Файлы ресурса | |
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Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Бикчентаев Айрат Мидхатович |
ru_RU |
| dc.contributor.author |
Moslehian Mohammad Sal |
ru_RU |
| dc.contributor.author |
Moslehian Mohammad Sal |
ru_RU |
| dc.date.accessioned |
2025-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2025-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2025 |
ru_RU |
| dc.identifier.citation |
Airat M. Bikchentaev, Mohammad Sal Moslehian, On pairs of projections //
Positivity, 2025, V. 29, no. 4. Paper No. 47. -- 13 pp. |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/?p_id=315890 |
ru_RU |
| dc.description.abstract |
POSITIVITY |
ru_RU |
| dc.description.abstract |
Two projections P and Q on a Hilbert space H are called acute if PQ < 1. We utilize the von Neumann alternating projection theorem to prove that if P and Q are acute, then P ∧ Q = 0. Conversely, if P ∧ Q = 0 and PQ is a compact operator, then P and Q are acute. An example is presented to show that the assumption of compactness is necessary. Let M be a von Neumann algebra, M pr be the lattice of all projections in M, and P, Q ∈ M pr . A pair (P, Q) is called modular in M pr if (R ∨ P) ∧ Q = (R ∧ Q) ∨ (P ∧ Q) for every R ∈ M pr with R ≤ Q. We present several characterizations of modular pairs of projections in a von Neumann algebra. In particular, for a factor M of type I or III, we investigate certain modularity conditions. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
Acute projections |
ru_RU |
| dc.subject |
modular projections |
ru_RU |
| dc.subject |
isoclinic projections |
ru_RU |
| dc.title |
On pairs of projections |
ru_RU |
| dc.type |
Статьи в зарубежных журналах и сборниках |
ru_RU |
|
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