| Форма представления | Статьи в зарубежных журналах и сборниках |
| Год публикации | 2019 |
| Язык | английский |
|
Бикчентаев Айрат Мидхатович, автор
|
|
Абед Сами Абдулла Абед, автор
|
| Библиографическое описание на языке оригинала |
Bikchentaev A.M., Abed S.A. Projections and Traces on von Neumann Algebras / A.M. Bikchentaev, S.A. Abed // Lobachevskii Journal of Mathematics. - 2019. - Vol. 40, No. 9. - P. 1260–1267. |
| Аннотация |
Let P,Q be projections on a Hilbert space. We prove the equivalence of the following conditions: (i) PQ + QP ≤ 2(QPQ)^p for some number 0 < p ≤ 1; (ii) PQ is paranormal; (iii) PQ is M*-paranormal; (iv) PQ = QP. This allows us to obtain the commutativity criterion for a von
Neumann algebra. For a positive normal functional ϕ on von Neumann algebra M it is proved the equivalence of the following conditions: (i) ϕ is tracial; (ii) ϕ(PQ + QP) ≤ 2ϕ((QPQ)^p) for all projections P,Q∈M and for some p = p(P,Q) ∈ (0, 1]; (iii) ϕ(PQP) ≤ ϕ(P)^{1/p}ϕ(Q)^{1/q} for
all projections P,Q∈M and some positive numbers p = p(P,Q), q = q(P,Q) with 1/p+ 1/q = 1, p = 2. Corollary: for a positive normal functional ϕ onMthe following conditions are equivalent: (i) ϕ is tracial; (ii) ϕ(A + A*) ≤ 2ϕ(|A*|) for all A∈M. |
| Ключевые слова |
Hilbert space, linear operator, projection, von Neumann algebra, positive functional, trace, operator inequality, commutativity |
| Название журнала |
Lobashevskii Journal of Mathematics
|
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=210046 |
| Файлы ресурса | |
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Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Бикчентаев Айрат Мидхатович |
ru_RU |
| dc.contributor.author |
Абед Сами Абдулла Абед |
ru_RU |
| dc.date.accessioned |
2019-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2019-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2019 |
ru_RU |
| dc.identifier.citation |
Bikchentaev A.M., Abed S.A. Projections and Traces on von Neumann Algebras / A.M. Bikchentaev, S.A. Abed // Lobachevskii Journal of Mathematics. - 2019. - Vol. 40, No. 9. - P. 1260–1267. |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/?p_id=210046 |
ru_RU |
| dc.description.abstract |
Lobashevskii Journal of Mathematics |
ru_RU |
| dc.description.abstract |
Let P,Q be projections on a Hilbert space. We prove the equivalence of the following conditions: (i) PQ + QP ≤ 2(QPQ)^p for some number 0 < p ≤ 1; (ii) PQ is paranormal; (iii) PQ is M*-paranormal; (iv) PQ = QP. This allows us to obtain the commutativity criterion for a von
Neumann algebra. For a positive normal functional ϕ on von Neumann algebra M it is proved the equivalence of the following conditions: (i) ϕ is tracial; (ii) ϕ(PQ + QP) ≤ 2ϕ((QPQ)^p) for all projections P,Q∈M and for some p = p(P,Q) ∈ (0, 1]; (iii) ϕ(PQP) ≤ ϕ(P)^{1/p}ϕ(Q)^{1/q} for
all projections P,Q∈M and some positive numbers p = p(P,Q), q = q(P,Q) with 1/p+ 1/q = 1, p = 2. Corollary: for a positive normal functional ϕ onMthe following conditions are equivalent: (i) ϕ is tracial; (ii) ϕ(A + A*) ≤ 2ϕ(|A*|) for all A∈M. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
Hilbert space |
ru_RU |
| dc.subject |
linear operator |
ru_RU |
| dc.subject |
projection |
ru_RU |
| dc.subject |
von Neumann algebra |
ru_RU |
| dc.subject |
positive functional |
ru_RU |
| dc.subject |
trace |
ru_RU |
| dc.subject |
operator inequality |
ru_RU |
| dc.subject |
commutativity |
ru_RU |
| dc.title |
Projections and Traces on von Neumann Algebras |
ru_RU |
| dc.type |
Статьи в зарубежных журналах и сборниках |
ru_RU |
|
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