KFU. Card publication. On pairs of projections

KAZAN
FEDERAL UNIVERSITY

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ON PAIRS OF PROJECTIONS

Form of presentation

Articles in international journals and collections

Year of publication

2025

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Other authors

Moslehian Mohammad Sal , author

Bibliographic description in the original language

Airat M. Bikchentaev, Mohammad Sal Moslehian, On pairs of projections // Positivity, 2025, V. 29, no. 4. Paper No. 47. -- 13 pp.

Annotation

Two projections P and Q on a Hilbert space H are called acute if PQ < 1. We utilize the von Neumann alternating projection theorem to prove that if P and Q are acute, then P ∧ Q = 0. Conversely, if P ∧ Q = 0 and PQ is a compact operator, then P and Q are acute. An example is presented to show that the assumption of compactness is necessary. Let M be a von Neumann algebra, M pr be the lattice of all projections in M, and P, Q ∈ M pr . A pair (P, Q) is called modular in M pr if (R ∨ P) ∧ Q = (R ∧ Q) ∨ (P ∧ Q) for every R ∈ M pr with R ≤ Q. We present several characterizations of modular pairs of projections in a von Neumann algebra. In particular, for a factor M of type I or III, we investigate certain modularity conditions.

Keywords

Acute projections, modular projections, isoclinic projections

The name of the journal

POSITIVITY

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

https://repository.kpfu.ru/eng/?p_id=315890&p_lang=2

Resource files

File name	Size (MB)	Format
F_Bik_mox_positivity25.pdf	0,24	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.contributor.author	Moslehian Mohammad Sal	ru_RU
dc.contributor.author	Moslehian Mohammad Sal	ru_RU
dc.date.accessioned	2025-01-01T00:00:00Z	ru_RU
dc.date.available	2025-01-01T00:00:00Z	ru_RU
dc.date.issued	2025	ru_RU
dc.identifier.citation	Airat M. Bikchentaev, Mohammad Sal Moslehian, On pairs of projections // Positivity, 2025, V. 29, no. 4. Paper No. 47. -- 13 pp.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=315890&p_lang=2	ru_RU
dc.description.abstract	POSITIVITY	ru_RU
dc.description.abstract	Two projections P and Q on a Hilbert space H are called acute if PQ < 1. We utilize the von Neumann alternating projection theorem to prove that if P and Q are acute, then P ∧ Q = 0. Conversely, if P ∧ Q = 0 and PQ is a compact operator, then P and Q are acute. An example is presented to show that the assumption of compactness is necessary. Let M be a von Neumann algebra, M pr be the lattice of all projections in M, and P, Q ∈ M pr . A pair (P, Q) is called modular in M pr if (R ∨ P) ∧ Q = (R ∧ Q) ∨ (P ∧ Q) for every R ∈ M pr with R ≤ Q. We present several characterizations of modular pairs of projections in a von Neumann algebra. In particular, for a factor M of type I or III, we investigate certain modularity conditions.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Acute projections	ru_RU
dc.subject	modular projections	ru_RU
dc.subject	isoclinic projections	ru_RU
dc.title	On pairs of projections	ru_RU
dc.type	Articles in international journals and collections	ru_RU