Form of presentation  Articles in international journals and collections 
Year of publication  2019 
Язык  английский 

Bikchentaev Ayrat Midkhatovich, author


Abed Sami Abdulla Abed, postgraduate kfu

Bibliographic description in the original language 
Bikchentaev A.M., Abed S.A. Projections and Traces on von Neumann Algebras / A.M. Bikchentaev, S.A. Abed // Lobachevskii Journal of Mathematics.  2019.  Vol. 40, No. 9.  P. 1260–1267. 
Annotation 
Let P,Q be projections on a Hilbert space. We prove the equivalence of the following conditions: (i) PQ + QP ≤ 2(QPQ)^p for some number 0 < p ≤ 1; (ii) PQ is paranormal; (iii) PQ is M*paranormal; (iv) PQ = QP. This allows us to obtain the commutativity criterion for a von
Neumann algebra. For a positive normal functional ϕ on von Neumann algebra M it is proved the equivalence of the following conditions: (i) ϕ is tracial; (ii) ϕ(PQ + QP) ≤ 2ϕ((QPQ)^p) for all projections P,Q∈M and for some p = p(P,Q) ∈ (0, 1]; (iii) ϕ(PQP) ≤ ϕ(P)^{1/p}ϕ(Q)^{1/q} for
all projections P,Q∈M and some positive numbers p = p(P,Q), q = q(P,Q) with 1/p+ 1/q = 1, p = 2. Corollary: for a positive normal functional ϕ onMthe following conditions are equivalent: (i) ϕ is tracial; (ii) ϕ(A + A*) ≤ 2ϕ(A*) for all A∈M. 
Keywords 
Hilbert space, linear operator, projection, von Neumann algebra, positive functional, trace, operator inequality, commutativity 
The name of the journal 
Lobashevskii Journal of Mathematics

Please use this ID to quote from or refer to the card 
https://repository.kpfu.ru/eng/?p_id=210046&p_lang=2 
Resource files  

Full metadata record 
Field DC 
Value 
Language 
dc.contributor.author 
Bikchentaev Ayrat Midkhatovich 
ru_RU 
dc.contributor.author 
Abed Sami Abdulla Abed 
ru_RU 
dc.date.accessioned 
20190101T00:00:00Z 
ru_RU 
dc.date.available 
20190101T00:00:00Z 
ru_RU 
dc.date.issued 
2019 
ru_RU 
dc.identifier.citation 
Bikchentaev A.M., Abed S.A. Projections and Traces on von Neumann Algebras / A.M. Bikchentaev, S.A. Abed // Lobachevskii Journal of Mathematics.  2019.  Vol. 40, No. 9.  P. 1260–1267. 
ru_RU 
dc.identifier.uri 
https://repository.kpfu.ru/eng/?p_id=210046&p_lang=2 
ru_RU 
dc.description.abstract 
Lobashevskii Journal of Mathematics 
ru_RU 
dc.description.abstract 
Let P,Q be projections on a Hilbert space. We prove the equivalence of the following conditions: (i) PQ + QP ≤ 2(QPQ)^p for some number 0 < p ≤ 1; (ii) PQ is paranormal; (iii) PQ is M*paranormal; (iv) PQ = QP. This allows us to obtain the commutativity criterion for a von
Neumann algebra. For a positive normal functional ϕ on von Neumann algebra M it is proved the equivalence of the following conditions: (i) ϕ is tracial; (ii) ϕ(PQ + QP) ≤ 2ϕ((QPQ)^p) for all projections P,Q∈M and for some p = p(P,Q) ∈ (0, 1]; (iii) ϕ(PQP) ≤ ϕ(P)^{1/p}ϕ(Q)^{1/q} for
all projections P,Q∈M and some positive numbers p = p(P,Q), q = q(P,Q) with 1/p+ 1/q = 1, p = 2. Corollary: for a positive normal functional ϕ onMthe following conditions are equivalent: (i) ϕ is tracial; (ii) ϕ(A + A*) ≤ 2ϕ(A*) for all A∈M. 
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 
von Neumann algebra 
ru_RU 
dc.subject 
positive functional 
ru_RU 
dc.subject 
trace 
ru_RU 
dc.subject 
operator inequality 
ru_RU 
dc.subject 
commutativity 
ru_RU 
dc.title 
Projections and Traces on von Neumann Algebras 
ru_RU 
dc.type 
Articles in international journals and collections 
ru_RU 
