KFU. Card publication. Differences of idempotents in C*-algebras and the quantum Hall effect. II. Unbounded idempotents

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DIFFERENCES OF IDEMPOTENTS IN C*-ALGEBRAS AND THE QUANTUM HALL EFFECT. II. UNBOUNDED IDEMPOTENTS

Form of presentation

Articles in international journals and collections

Year of publication

2024

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Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Authors, postgraduates KFU

Khadur Makhmud -, postgraduate kfu

Bibliographic description in the original language

A.M. Bikchentaev, Mahmoud Khadour, Differences of idempotents in C*-algebras and the quantum Hall effect. II. Unbounded idempotents // Lobachevskii Journal of Mathematics, 2024, Vol. 45, No. 4, pp. 1825–1832.

Annotation

Let a von Neumann algebra M of operators act on a Hilbert space H, I be the unit of M, τ be a faithful semifinite normal trace on M. Let (M, τ) be the ∗-algebra of all τ-measurable operators and L1(M, τ) be the Banach space of all τ-integrable operators, P, Q ∈ S(M, τ) be idempotents. If P − Q ∈ L1(M, τ) then τ(P − Q) ∈ R. In particular, if A = A3 ∈ L1(M, τ), then τ(A) ∈ R. If P − Q ∈ L1(M, τ) and P Q ∈ M, then for all n ∈ N we have (P − Q)2n+1 ∈ L1(M, τ) and τ((P − Q)2n+1) = τ(P − Q) ∈ R. If A ∈ L2(M, τ) and U ∈ M is an isometry, then ||UA − A||22 ≤ 2||(I − U)AA∗||1.

Keywords

Hilbert space, von Neumann algebra, normal trace, measurable operator, idempotent, tripotent, quantum Hall effect

The name of the journal

Lobachevskii Journal of Mathematics

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/184030/LOJM1825.pdf?sequence=1&isAllowed=y

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

https://repository.kpfu.ru/eng/?p_id=302205&p_lang=2

Resource files

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LOJM1825.pdf	0,53	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.contributor.author	Khadur Makhmud -	ru_RU
dc.date.accessioned	2024-01-01T00:00:00Z	ru_RU
dc.date.available	2024-01-01T00:00:00Z	ru_RU
dc.date.issued	2024	ru_RU
dc.identifier.citation	A.M. Bikchentaev, Mahmoud Khadour, Differences of idempotents in C*-algebras and the quantum Hall effect. II. Unbounded idempotents // Lobachevskii Journal of Mathematics, 2024, Vol. 45, No. 4, pp. 1825–1832.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=302205&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	Let a von Neumann algebra M of operators act on a Hilbert space H, I be the unit of M, τ be a faithful semifinite normal trace on M. Let (M, τ) be the ∗-algebra of all τ-measurable operators and L1(M, τ) be the Banach space of all τ-integrable operators, P, Q ∈ S(M, τ) be idempotents. If P − Q ∈ L1(M, τ) then τ(P − Q) ∈ R. In particular, if A = A3 ∈ L1(M, τ), then τ(A) ∈ R. If P − Q ∈ L1(M, τ) and P Q ∈ M, then for all n ∈ N we have (P − Q)2n+1 ∈ L1(M, τ) and τ((P − Q)2n+1) = τ(P − Q) ∈ R. If A ∈ L2(M, τ) and U ∈ M is an isometry, then \|\|UA − A\|\|22 ≤ 2\|\|(I − U)AA∗\|\|1.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	normal trace	ru_RU
dc.subject	measurable operator	ru_RU
dc.subject	idempotent	ru_RU
dc.subject	tripotent	ru_RU
dc.subject	quantum Hall effect	ru_RU
dc.title	Differences of idempotents in C*-algebras and the quantum Hall effect. II. Unbounded idempotents	ru_RU
dc.type	Articles in international journals and collections	ru_RU