| Form of presentation | Articles in international journals and collections |
| Year of publication | 2025 |
| Язык | английский |
|
Bikchentaev Ayrat Midkhatovich, author
|
|
Moslehian Mohammad Sal, author
|
| Bibliographic description in the original language |
Airat M. Bikchentaev and Mohammad Sal Moslehian,
Characterizations of tracial functionals on $C^*$-algebras,
Infinite Dimensional Analysis, Quantum Probability and Related Topics
(2025) Vol. 28, no 1. 2550003 (14 pages) World Scientific Publishing Company
DOI: 10.1142/S0219025725500031 |
| Annotation |
We establish several characterizations of tracial functionals φ on the finite C∗-algebra 𝕄n (that is, φ=k tr for some number k>0) via any one of the inequalities φ(AαB1−α)≤αφ(A)+(1−α)φ(B) and φ(|eA|)≤φ(eReA), which are well-known when φ=tr.
In addition, we characterize the trace on 𝕄n among all positive linear functionals φ with φ(I)=n through an inequality for determinant. We lso establish that such a functional is equal to the usual trace if and only if φ((B12AB12)m)≤φ(A)mφ(B)m for all positive integers m and all A,B∈𝕄n+. Furthermore, we show that there is no state φ on 𝕄n,n≥2 such that φ(B1/2AB1/2)≤φ(A)φ(B) for all A,B∈𝕄n+.
Finally, we establish that for a positive linear functional
φ
on a
C
∗
-algebra
𝒜
, the following conditions are equivalent: (i)
φ
is tracial; (ii)
φ
(
e
A
B
−
I
)
≥
0
for all
A
,
B
∈
𝒜
+
. A new criterion for the commutativity of
C
∗
-algebras is also provided. |
| Keywords |
Hilbert space, von Neumann algebra, trace, tracial inequality, matrix, positive linear functional |
| The name of the journal |
Infinite Dimensional Analysis, Quantum Probability and Related Topics
|
| Please use this ID to quote from or refer to the card |
https://repository.kpfu.ru/eng/?p_id=312585&p_lang=2 |
| Resource files | |
|
|
Full metadata record  |
| Field DC |
Value |
Language |
| dc.contributor.author |
Bikchentaev Ayrat Midkhatovich |
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 and Mohammad Sal Moslehian,
Characterizations of tracial functionals on $C^*$-algebras,
Infinite Dimensional Analysis, Quantum Probability and Related Topics
(2025) Vol. 28, no 1. 2550003 (14 pages) World Scientific Publishing Company
DOI: 10.1142/S0219025725500031 |
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/eng/?p_id=312585&p_lang=2 |
ru_RU |
| dc.description.abstract |
Infinite Dimensional Analysis, Quantum Probability and Related Topics |
ru_RU |
| dc.description.abstract |
We establish several characterizations of tracial functionals φ on the finite C∗-algebra 𝕄n (that is, φ=k tr for some number k>0) via any one of the inequalities φ(AαB1−α)≤αφ(A)+(1−α)φ(B) and φ(|eA|)≤φ(eReA), which are well-known when φ=tr.
In addition, we characterize the trace on 𝕄n among all positive linear functionals φ with φ(I)=n through an inequality for determinant. We lso establish that such a functional is equal to the usual trace if and only if φ((B12AB12)m)≤φ(A)mφ(B)m for all positive integers m and all A,B∈𝕄n+. Furthermore, we show that there is no state φ on 𝕄n,n≥2 such that φ(B1/2AB1/2)≤φ(A)φ(B) for all A,B∈𝕄n+.
Finally, we establish that for a positive linear functional
φ
on a
C
∗
-algebra
𝒜
, the following conditions are equivalent: (i)
φ
is tracial; (ii)
φ
(
e
A
B
−
I
)
≥
0
for all
A
,
B
∈
𝒜
+
. A new criterion for the commutativity of
C
∗
-algebras is also provided. |
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
Hilbert space |
ru_RU |
| dc.subject |
von Neumann algebra |
ru_RU |
| dc.subject |
trace |
ru_RU |
| dc.subject |
tracial inequality |
ru_RU |
| dc.subject |
matrix |
ru_RU |
| dc.subject |
positive linear functional |
ru_RU |
| dc.title |
Characterizations of tracial functionals on $C^*$-algebras |
ru_RU |
| dc.type |
Articles in international journals and collections |
ru_RU |
|
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