KFU. Card publication. Seminorms Associated with Subadditive Weights on С*-Algebras

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SEMINORMS ASSOCIATED WITH SUBADDITIVE WEIGHTS ON С*-ALGEBRAS

Form of presentation

Articles in international journals and collections

Year of publication

2020

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

A. M. Bikchentaev, Seminorms Associated with Subadditive Weights on S*-Algebras // Mathematical Notes, 2020, Vol. 107, No. 3, pp. 383--391.

Annotation

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.

Keywords

Hilbert space, bounded linear operator, Cayley transform, projection, von Neumann algebra, C*-algebra, subadditive weight, seminorm, matrix norm.

The name of the journal

MATHEMATICAL NOTES

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

https://repository.kpfu.ru/eng/?p_id=228625&p_lang=2

Resource files

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MTN383.pdf	0,62	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	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/eng/?p_id=228625&p_lang=2	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	Articles in international journals and collections	ru_RU