| Форма представления | Статьи в зарубежных журналах и сборниках |
| Год публикации | 2020 |
| Язык | английский |
|
Бикчентаев Айрат Мидхатович, автор
|
| Библиографическое описание на языке оригинала |
A. M. Bikchentaev, Seminorms Associated with Subadditive Weights
on С*-Algebras // Mathematical Notes, 2020, Vol. 107, No. 3, pp. 383--391. |
| Аннотация |
Let $\varphi$ be a subadditive weight on a C*-algebra $A$, and let $M_\varphi$ be the set of all elements $x$ in $A^+$ with $\varphi (x)<+\infty$. A seminorm $\|\cdot\|_\varphi$ is introduced on the lineal $lin_R M^+_\varphi$, and a
sufficient condition for the seminorm to be a norm is given. Let $I$ be the unit of the algebra $A$, and
let $\varphi(I) = 1$. Then, for every element $x$ of $A^{sa}, the limit $\pho_\varphi (x) = \lim_{t \to 0+} (\varphi (I + tx) - 1)/t$ exists
and is finite. Properties of $\pho_\varphi$ are investigated, and examples of subadditive weights on C*-algebras are considered. On the basis of Lozinskii's 1958 results, specific subadditive weights on $M_n(C)$
are considered. An estimate for the difference of Cayley transforms of Hermitian elements of a von Neumann algebra is obtained. |
| Ключевые слова |
Hilbert space, bounded linear operator, Cayley transform, projection, von Neumann algebra, C*-algebra, subadditive weight, seminorm, matrix norm.
|
| Название журнала |
MATHEMATICAL NOTES
|
| Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку |
https://repository.kpfu.ru/?p_id=228625 |
| Файлы ресурса | |
|
|
Полная запись метаданных  |
| Поле DC |
Значение |
Язык |
| dc.contributor.author |
Бикчентаев Айрат Мидхатович |
ru_RU |
| dc.date.accessioned |
2020-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2020-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2020 |
ru_RU |
| dc.identifier.citation |
A. M. Bikchentaev, Seminorms Associated with Subadditive Weights
on С*-Algebras // Mathematical Notes, 2020, Vol. 107, No. 3, pp. 383--391. |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/?p_id=228625 |
ru_RU |
| dc.description.abstract |
MATHEMATICAL NOTES |
ru_RU |
| dc.description.abstract |
Let $\varphi$ be a subadditive weight on a C*-algebra $A$, and let $M_\varphi$ be the set of all elements $x$ in $A^+$ with $\varphi (x)<+\infty$. A seminorm $\|\cdot\|_\varphi$ is introduced on the lineal $lin_R M^+_\varphi$, and a
sufficient condition for the seminorm to be a norm is given. Let $I$ be the unit of the algebra $A$, and
let $\varphi(I) = 1$. Then, for every element $x$ of $A^{sa}, the limit $\pho_\varphi (x) = \lim_{t \to 0+} (\varphi (I + tx) - 1)/t$ exists
and is finite. Properties of $\pho_\varphi$ are investigated, and examples of subadditive weights on C*-algebras are considered. On the basis of Lozinskii's 1958 results, specific subadditive weights on $M_n(C)$
are considered. An estimate for the difference of Cayley transforms of Hermitian elements of a von Neumann algebra is obtained. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
Hilbert space |
ru_RU |
| dc.subject |
bounded linear operator |
ru_RU |
| dc.subject |
Cayley transform |
ru_RU |
| dc.subject |
projection |
ru_RU |
| dc.subject |
von Neumann algebra |
ru_RU |
| dc.subject |
C*-algebra |
ru_RU |
| dc.subject |
subadditive weight |
ru_RU |
| dc.subject |
seminorm |
ru_RU |
| dc.subject |
matrix norm.
|
ru_RU |
| dc.title |
Seminorms Associated with Subadditive Weights
on С*-Algebras |
ru_RU |
| dc.type |
Статьи в зарубежных журналах и сборниках |
ru_RU |
|
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