Annals of Functional Analysis

Conic structure of the non-negative operator convex functions on $(0,\infty)$

Uwe Franz and Fumio Hiai

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The conic structure of the convex cone of non-negative operator convex functions on $(0,\infty)$ (also on $(-1,1)$) is clarified. We completely determine the extreme rays, the closed faces, and the simplicial closed faces of this convex cone.

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Ann. Funct. Anal., Volume 5, Number 2 (2014), 158-175.

First available in Project Euclid: 7 April 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
Secondary: 47A60: Functional calculus

Operator convex function operator monotone function convex cone extreme ray facial cone simplicial cone


Franz, Uwe; Hiai, Fumio. Conic structure of the non-negative operator convex functions on $(0,\infty)$. Ann. Funct. Anal. 5 (2014), no. 2, 158--175. doi:10.15352/afa/1396833511.

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