KFU. Card publication. Ideal $F$-norms on $C^*$-algebras. II

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FEDERAL UNIVERSITY

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

Form of presentation

Articles in international journals and collections

Year of publication

2019

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

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

Annotation

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 $\mathcal{A}$.

Keywords

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

The name of the journal

Russian Mathematics

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=198020&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	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/eng/?p_id=198020&p_lang=2	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	Articles in international journals and collections	ru_RU