Title : ( Characterization of Tracial Functionals on von Neumann Algebras )
Authors: A. M. Bikchentaev , Mohammad Sal Moslehian , V. Zh. Sakbaev ,
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Abstract
Inspired by the condition supλ∈C ||eλY Xe−λY || < ∞, which is equivalent to the com- mutativity of two operators X, Y ∈ B(H), we establish that for a state φ on a von Neumann algebra M the following conditions are equivalent: (i) φ is tracial; (ii) supλ∈C |φ(e λY Xe−λY )| < ∞ for all positive operators X, Y ∈ M; (iii) |φ(Re(X 2 )| ≤ φ(X ∗ X) for all X ∈ M; (iv) φ(X ∗Y + Y ∗X) = φ(XY ∗ + Y X ∗ ) for all unitary operators X, Y ∈ M. We also provide new criteria for the commutativity of von Neumann algebras.
Keywords
, Hilbert space, linear operator, von Neumann algebra, trace, tracial inequality, matrix
@article{paperid:1104613,
author = {آ. م. بیکچنتائف and Sal Moslehian, Mohammad and و. ژ. ساکبائف},
title = {Characterization of Tracial Functionals on von Neumann Algebras},
journal = {Lobachevskii Journal of Mathematics},
year = {2025},
volume = {46},
number = {6},
month = {September},
issn = {1995-0802},
pages = {2484--2488},
numpages = {4},
keywords = {Hilbert space; linear operator; von Neumann algebra; trace; tracial
inequality; matrix},
}
%0 Journal Article
%T Characterization of Tracial Functionals on von Neumann Algebras
%A آ. م. بیکچنتائف
%A Sal Moslehian, Mohammad
%A و. ژ. ساکبائف
%J Lobachevskii Journal of Mathematics
%@ 1995-0802
%D 2025
