Partial Orders in Non-commutative $$L^p$$ Spaces Associated with Semi-finite von Neumann Algebras

2021 ◽  
Author(s):  
Xinhui Wang ◽  
Guoxing Ji
Keyword(s):  
Von Neumann Algebras ◽  
Partial Orders ◽  
Von Neumann ◽  
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.

scholarly journals INTEGER OPERATORS IN FINITE VON NEUMANN ALGEBRAS

2011 ◽  
Vol 03 (04) ◽  
pp. 433-450
Author(s):  
ANDREAS THOM
Keyword(s):  
Potential Theory ◽  
Spectral Properties ◽  
Von Neumann Algebras ◽  
Logarithmic Capacity ◽  
Integral Group ◽  
Von Neumann ◽  
Classical Potential ◽  
Classical Potential Theory ◽  
Adjoint Operators ◽  
Finite Von Neumann Algebras

Motivated by the study of spectral properties of self-adjoint operators in the integral group ring of a sofic group, we define and study integer operators. We establish a relation with classical potential theory and in particular the circle of results obtained by Fekete and Szegö, see [3, 4, 13]. More concretely, we use results by Rumely, see [12], on equidistribution of algebraic integers to obtain a description of those integer operator which have spectrum of logarithmic capacity less than or equal to one. Finally, we relate the study of integer operators to a recent construction by Petracovici and Zaharescu, see [10].

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