Form of presentation  Articles in international journals and collections 
Year of publication  2022 
Язык  английский 

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language 
Bikchentaev A.M. Invertibility of the Operators on Hilbert Spaces
and Ideals in C*Algebras // Mathematical Notes, 2022, Vol. 112, No. 3, pp. 24–32. 
Annotation 
Let H be a Hilbert space over the field C, and let B(H) be the ∗algebra of all linear bounded operators in H. Sufficient conditions for the positivity and invertibility of operators
from B(H) are found. An arbitrary symmetry from a von Neumann algebra A is written as the product A^{−1}UA with a positive invertible A and a selfadjoint unitary U from A. Let $\varphi$ be the weight on a von Neumann algebra A, let A ∈ A, and let $\ A \ ≤ 1$. If $A^*A−I ∈ N_{\varphi}$, then $AI\in N_{\varphi}$ and, for any isometry U ∈ A, the inequality $\A − U\_{\varphi, 2} ≥ \ A − I\_{\varphi, 2}$ holds. If U is a unitary operator from the polar expansion of the invertible operator A, then this inequality becomes an equality. 
Keywords 
Hilbert space, linear operator, invertible operator, von Neumann algebra, Calgebra, weight. 
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=269301&p_lang=2 
Resource files  

Full metadata record 
Field DC 
Value 
Language 
dc.contributor.author 
Bikchentaev Ayrat Midkhatovich 
ru_RU 
dc.date.accessioned 
20220101T00:00:00Z 
ru_RU 
dc.date.available 
20220101T00:00:00Z 
ru_RU 
dc.date.issued 
2022 
ru_RU 
dc.identifier.citation 
Bikchentaev A.M. Invertibility of the Operators on Hilbert Spaces
and Ideals in C*Algebras // Mathematical Notes, 2022, Vol. 112, No. 3, pp. 24–32. 
ru_RU 
dc.identifier.uri 
https://repository.kpfu.ru/eng/?p_id=269301&p_lang=2 
ru_RU 
dc.description.abstract 
MATHEMATICAL NOTES 
ru_RU 
dc.description.abstract 
Let H be a Hilbert space over the field C, and let B(H) be the ∗algebra of all linear bounded operators in H. Sufficient conditions for the positivity and invertibility of operators
from B(H) are found. An arbitrary symmetry from a von Neumann algebra A is written as the product A^{−1}UA with a positive invertible A and a selfadjoint unitary U from A. Let $\varphi$ be the weight on a von Neumann algebra A, let A ∈ A, and let $\ A \ ≤ 1$. If $A^*A−I ∈ N_{\varphi}$, then $AI\in N_{\varphi}$ and, for any isometry U ∈ A, the inequality $\A − U\_{\varphi, 2} ≥ \ A − I\_{\varphi, 2}$ holds. If U is a unitary operator from the polar expansion of the invertible operator A, then this inequality becomes an equality. 
ru_RU 
dc.language.iso 
ru 
ru_RU 
dc.subject 
Hilbert space 
ru_RU 
dc.subject 
linear operator 
ru_RU 
dc.subject 
invertible operator 
ru_RU 
dc.subject 
von Neumann algebra 
ru_RU 
dc.subject 
Calgebra 
ru_RU 
dc.subject 
weight. 
ru_RU 
dc.title 
Invertibility of the Operators on Hilbert Spaces
and Ideals in C*Algebras 
ru_RU 
dc.type 
Articles in international journals and collections 
ru_RU 
