ON EQUALITY CONDITION FOR TRACE JENSEN INEQUALITY IN SEMI-FINITE VON NEUMANN ALGEBRAS
2008 ◽
Vol 19
(04)
◽
pp. 481-501
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Keyword(s):
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.
2013 ◽
Vol 56
(1)
◽
pp. 9-12
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2001 ◽
Vol 12
(06)
◽
pp. 743-750
◽
2002 ◽
Vol 65
(1)
◽
pp. 79-91
◽
2002 ◽
Vol 132
(1)
◽
pp. 137-154
◽
2011 ◽
Vol 2011
◽
pp. 1-24
Keyword(s):