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Trace inequalities for spaces in spectral duality

Tom 104 / 1993

O. E. Tikhonov Studia Mathematica 104 (1993), 99-110 DOI: 10.4064/sm-104-1-99-110

Streszczenie

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.

Autorzy

  • O. E. Tikhonov

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