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.
@article{bwmeta1.element.bwnjournal-article-smv104i1p99bwm,
author = {O. Tikhonov},
title = {Trace inequalities for spaces in spectral duality},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {99-110},
zbl = {0812.47033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv104i1p99bwm}
}
Tikhonov, O. Trace inequalities for spaces in spectral duality. Studia Mathematica, Tome 104 (1993) pp. 99-110. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i1p99bwm/
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