scholarly journals On Power-Bounded Operators in Finite von Neumann Algebras

1996 ◽  
Vol 141 (1) ◽  
pp. 133-158 ◽  
Author(s):  
Gilles Cassier ◽  
Thierry Fack
Keyword(s):  
Von Neumann Algebras ◽  
Bounded Operators ◽  
Von Neumann ◽  
Power Bounded Operators ◽  
Finite Von Neumann Algebras ◽  
Power Bounded

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.

Two Consequences of Brunel's Theorem

1991 ◽  
Vol 34 (1) ◽  
pp. 105-108
Author(s):  
James H. Olsen
Keyword(s):  
Ergodic Theorem ◽  
Bounded Operators ◽  
Positive Power ◽  
Multiple Sequence ◽  
Power Bounded Operators ◽  
Recent Theorem ◽  
The Individual ◽  
Power Bounded

AbstractIn this note we observe two consequences of Brunei's recent theorem. If T1,..., Tn are majorized by positive power-bounded operators S1,..., Sn of Lp, 1 < p < ∞, for which the ergodic theorem holds, then a multiple sequence ergodic theorem holds for T1,....,Tn. Further, the individual convergence for each Tk can be taken along uniform sequences.

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