Geodesic
Trace inequalities for spaces in spectral duality
Studia Mathematica, Tome 104 (1993) no. 1, pp. 99-110
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Let (A,e) and (V,K) be an order-unit space and a base-norm space in spectral duality, as in noncommutative spectral theory of Alfsen and Shultz. Let t be a norm lower semicontinuous trace on A, and let φ be a nonnegative convex function on ℝ. It is shown that the mapping a → t(φ(a)) is convex on A. Moreover, the mapping is shown to be nondecreasing if so is φ. Some other similar statements concerning traces and real-valued functions are also obtained. 
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O. E. Tikhonov. Trace inequalities for spaces in spectral duality. Studia Mathematica, Tome 104 (1993) no. 1, pp. 99-110. doi: 10.4064/sm-104-1-99-110

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