If A is a normed power-associative complex algebra such that the selfadjoint part is normally ordered with respect to some order, then the Korovkin closure (see the introduction for definitions) of T ∪ {t* ∘ t| t ∈ T} contains J*(T) for any subset T of A. This can be applied to C*-algebras, minimal norm ideals on a Hilbert space, and to H*-algebras. For bounded H*-algebras and dual C*-algebras there is even equality. This answers a question posed in [1].
@article{bwmeta1.element.bwnjournal-article-smv100i3p219bwm,
author = {Ferdinand Beckhoff},
title = {Korovkin theory in normed algebras},
journal = {Studia Mathematica},
volume = {100},
year = {1991},
pages = {219-228},
zbl = {0831.46059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv100i3p219bwm}
}
Beckhoff, Ferdinand. Korovkin theory in normed algebras. Studia Mathematica, Tome 100 (1991) pp. 219-228. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv100i3p219bwm/
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