TRACE JENSEN INEQUALITY FOR SELF-ADJOINT OPERATORS IN SEMI-FINITE VON NEUMANN ALGEBRAS

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  • HIDEKI KOSAKI
    Graduate School of Mathematics, Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan

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<jats:p> Let [Formula: see text] be a semi-finite von Neumann algebra equipped with a faithful semi-finite normal trace τ, and f(t) be a convex function with f(0) = 0. The trace Jensen inequality in our previous work states τ(f(a*xa)) ≤ τ(a*f(x)a) (as long as the both sides are well-defined) for a contraction [Formula: see text] and a semi-bounded τ-measurable operator x. Validity of this inequality for (not necessarily semi-bounded) self-adjoint τ-measurable operators is investigated. </jats:p>

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