scholarly journals Characterization of singular numbers of products of operators in matrix algebras and finite von Neumann algebras

2015 ◽  
Vol 139 (4) ◽  
pp. 400-419 ◽  
Author(s):  
H. Bercovici ◽  
B. Collins ◽  
K. Dykema ◽  
W.S. Li
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann ◽  
Matrix Algebras ◽  
Singular Numbers ◽  
Finite Von Neumann Algebras

scholarly journals ON EQUALITY CONDITION FOR TRACE JENSEN INEQUALITY IN SEMI-FINITE VON NEUMANN ALGEBRAS

2008 ◽  
Vol 19 (04) ◽  
pp. 481-501 ◽  
Author(s):  
TETSUO HARADA ◽  
HIDEKI KOSAKI
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Adjoint Operator ◽  
Strict Convexity ◽  
Jensen Inequality ◽  
Von Neumann ◽  
Convexity Assumption ◽  
Finite Von Neumann Algebra ◽  
Equality Condition ◽  
Finite Von Neumann Algebras

Let τ be a faithful semi-finite normal trace on a semi-finite von Neumann algebra, and f(t) be a convex function with f(0) = 0. The trace Jensen inequality states τ(f(a* xa)) ≤ τ(a* f(x)a) for a contraction a and a self-adjoint operator x. Under certain strict convexity assumption on f(t), we will study when this inequality reduces to the equality.

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