Title : ( Characterizations of the canonical trace on full matrix algebras )
Authors: Mohammad Sal Moslehian , Airat M. Bikchentaev ,
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Abstract
We establish that a positive linear functional on the full matrix algebra Mn is a positive multiple of the canonical trace if and only if φ(A) = φ(|A|) implies that A is positive semidefinite. Furthermore, we characterize the canonical trace on Mn among all positive linear functionals φ on Mn with φ(I) = n via Yang’s inequality φ(A1/2 BA1/2)1/2 ≤ φ(A + B)/2, where A, B ∈ Mn are positive semidefinite matrices.
Keywords
Trace Yang’s inequality Positive semidefinite Characterization
@article{paperid:1103393,
author = {Sal Moslehian, Mohammad and آیرات بیکچنتائف},
title = {Characterizations of the canonical trace on full matrix algebras},
journal = {Journal of Mathematical Analysis and Applications},
year = {2025},
volume = {552},
number = {2},
month = {December},
issn = {0022-247X},
pages = {129764--129773},
numpages = {9},
keywords = {Trace
Yang’s inequality
Positive semidefinite
Characterization},
}
%0 Journal Article
%T Characterizations of the canonical trace on full matrix algebras
%A Sal Moslehian, Mohammad
%A آیرات بیکچنتائف
%J Journal of Mathematical Analysis and Applications
%@ 0022-247X
%D 2025
