Abstract
Let ℋ be a group of *-automorphisms on the algebra of bounded linear operators on a complex Hilbert space H. Then the strongly closed convex hull of the orbit of any compact operator under ℋ consists of compact operators. The same is true if one replaces “compact” by “nuclear”, “Hilbert-Schmidt” or “positive Fredholm”. We further discuss these results in the framework of the noncommutative mean ergodic theorem of KOVACS and SZ#x00FC;CS and formulate an analogous theorem for the algebra of compact operators on a complex Hilbert space.
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Gefördert von der Deutschen Forschungsgemeinschaft im Rahmen des Forschungsvorhabens Ko 506/1.
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Tischer, J., Wittmer, H. Invarianz gewisser Operatorenklassen unter nichtkommutativen ergodischen Mitteln. Manuscripta Math 13, 73–81 (1974). https://doi.org/10.1007/BF01168744
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DOI: https://doi.org/10.1007/BF01168744