We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of Lieb type and symmetric (anti-) norm functions of the form , where Φ and Ψ are positive linear maps, σ is an operator mean, and 94ab21aca66db9e" title="Click to view the MathML source">f(xγ) with a certain power γ is an operator monotone function on (0,∞). Moreover, the variational method of Carlen, Frank and Lieb is extended to general non-decreasing convex/concave functions on (0,∞) so that we prove joint concavity/convexity of more trace functions of Lieb type.
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