| Форма представления | Статьи в зарубежных журналах и сборниках |
| Год публикации | 2026 |
| Язык | английский |
|
Бикчентаев Айрат Мидхатович, автор
|
|
Moslehian Mohammad Sal , автор
|
| Библиографическое описание на языке оригинала |
Airat M. Bikchentaev, Mohammad Sal Moslehian,
Trace inequalities and characterizations of tracial
functionals in operator algebras // Positivity (2026) V. 30, Article 24. 15 p. |
| Аннотация |
For a positive normal linear functional ϕ on a von Neumann algebra A , we prove that the following conditions are equivalent: (i) ϕ is tracial, (ii) |ϕ(Re(A2)| ≤ ϕ(|A|2)
for all A ∈ A , and (iii) |ϕ(A2)| ≤ ϕ(|A|2) for all A ∈ A . Based on this result,
we present some criteria for commutativity of a von Neumann algebra. For a trace ϕ
on a C∗-algebra A , we prove that −ϕ(A2B2) ≤ ϕ((AB)2) ≤ ϕ(A2B2) for certain elements of A , and show that when ϕ is faithful, the equality in the second inequality
is achieved if and only if AB = BA. Moreover, we partially generalize the Araki–Lieb–Thirring inequality to arbitrary traces on any C∗-algebras and to self-adjoint elements. Furthermore, we present a simple joint proof for Tr(AB) ? Tr(X∗X) ≤
Tr(A) Tr(B) ? Tr(X∗) Tr(X) provided that A XX∗ B is positive semidefinite, without using the fact that (X) = X + (Tr X)I is completely copositive, and then present a characterization of the trace on the full matrix algebra Mn. |
| Ключевые слова |
C∗-algebra, von Neumann algebra, trace, positive linear functional,
positive semidefinite block matrix |
| Название журнала |
POSITIVITY
|
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=324508 |
| Файлы ресурса | |
|
|
Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Бикчентаев Айрат Мидхатович |
ru_RU |
| dc.contributor.author |
Moslehian Mohammad Sal |
ru_RU |
| dc.date.accessioned |
2026-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2026-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2026 |
ru_RU |
| dc.identifier.citation |
Airat M. Bikchentaev, Mohammad Sal Moslehian,
Trace inequalities and characterizations of tracial
functionals in operator algebras // Positivity (2026) V. 30, Article 24. 15 p. |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/?p_id=324508 |
ru_RU |
| dc.description.abstract |
POSITIVITY |
ru_RU |
| dc.description.abstract |
For a positive normal linear functional ϕ on a von Neumann algebra A , we prove that the following conditions are equivalent: (i) ϕ is tracial, (ii) |ϕ(Re(A2)| ≤ ϕ(|A|2)
for all A ∈ A , and (iii) |ϕ(A2)| ≤ ϕ(|A|2) for all A ∈ A . Based on this result,
we present some criteria for commutativity of a von Neumann algebra. For a trace ϕ
on a C∗-algebra A , we prove that −ϕ(A2B2) ≤ ϕ((AB)2) ≤ ϕ(A2B2) for certain elements of A , and show that when ϕ is faithful, the equality in the second inequality
is achieved if and only if AB = BA. Moreover, we partially generalize the Araki–Lieb–Thirring inequality to arbitrary traces on any C∗-algebras and to self-adjoint elements. Furthermore, we present a simple joint proof for Tr(AB) ? Tr(X∗X) ≤
Tr(A) Tr(B) ? Tr(X∗) Tr(X) provided that A XX∗ B is positive semidefinite, without using the fact that (X) = X + (Tr X)I is completely copositive, and then present a characterization of the trace on the full matrix algebra Mn. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
C∗-algebra |
ru_RU |
| dc.subject |
von Neumann algebra |
ru_RU |
| dc.subject |
trace |
ru_RU |
| dc.subject |
positive linear functional |
ru_RU |
| dc.subject |
positive semidefinite block matrix |
ru_RU |
| dc.title |
Trace inequalities and characterizations of tracial
functionals in operator algebras |
ru_RU |
| dc.type |
Статьи в зарубежных журналах и сборниках |
ru_RU |
|
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