КФУ. Карточка публикации. Ideal $F$-norms on $C^*$-algebras. II

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IDEAL $F$-NORMS ON $C^*$-ALGEBRAS. II

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2019

Язык

английский

Авторы, сотрудники КФУ

Бикчентаев Айрат Мидхатович, автор

Библиографическое описание на языке оригинала

A.M. Bikchentaev, Ideal $F$-norms on $C^*$-algebras. II // Russian Mathematics, 2019, Vol. 63, No. 3. P. 78-82.

Аннотация

We study ideal $F$-norms $\|\cdot\|_p$, $0 < p <+\infty$ associated with a trace $\varphi$ on a $C^*$-algebra $\mathcal{A}$. If $A, B$ of $\mathcal{A}$ are such that $|A|\leq |B|$, then $\|A\|_p \leq \|B\|_p$. We have $\|A\|_p=\|A^*\|_p$ for all $A$ from $\mathcal{A}$ ($0 < p <+\infty$) and a seminorm $\|\cdot\|_p$ for $1 \leq p <+\infty$. We estimate the distance from any element of a unital $\mathcal{A}$ to the scalar subalgebra in the seminorm $\|\cdot\|_1$. We investigate geometric properties of semiorthogonal projections from $\mathcal{A}$. If a trace $\varphi$ is finite, then the set of all finite sums of pairwise products of projections and semiorthogonal projections (in any order) of $\mathcal{A}$ with coefficients from $\mathbb{R}^+ $ is not dense in $\mathcal{A}$.

Ключевые слова

Hilbert space, linear operator, projection, semiorthogonal projection, unitary operator, inequality, $C^*$-algebra, trace, ideal $F$-norm.

Название журнала

Russian Mathematics

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https://repository.kpfu.ru/?p_id=198020

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Бикчентаев Айрат Мидхатович	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	A.M. Bikchentaev, Ideal $F$-norms on $C^*$-algebras. II // Russian Mathematics, 2019, Vol. 63, No. 3. P. 78-82.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=198020	ru_RU
dc.description.abstract	Russian Mathematics	ru_RU
dc.description.abstract	We study ideal $F$-norms $\\|\cdot\\|_p$, $0 < p <+\infty$ associated with a trace $\varphi$ on a $C^$-algebra $\mathcal{A}$. If $A, B$ of $\mathcal{A}$ are such that $\|A\|\leq \|B\|$, then $\\|A\\|_p \leq \\|B\\|_p$. We have $\\|A\\|_p=\\|A^\\|_p$ for all $A$ from $\mathcal{A}$ ($0 < p <+\infty$) and a seminorm $\\|\cdot\\|_p$ for $1 \leq p <+\infty$. We estimate the distance from any element of a unital $\mathcal{A}$ to the scalar subalgebra in the seminorm $\\|\cdot\\|_1$. We investigate geometric properties of semiorthogonal projections from $\mathcal{A}$. If a trace $\varphi$ is finite, then the set of all finite sums of pairwise products of projections and semiorthogonal projections (in any order) of $\mathcal{A}$ with coefficients from $\mathbb{R}^+ $ is not dense in $\mathcal{A}$.	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	semiorthogonal projection	ru_RU
dc.subject	unitary operator	ru_RU
dc.subject	inequality	ru_RU
dc.subject	$C^*$-algebra	ru_RU
dc.subject	trace	ru_RU
dc.subject	ideal $F$-norm.	ru_RU
dc.title	Ideal $F$-norms on $C^*$-algebras. II	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU