Geodesic
Korovkin theory in normed algebras
Studia Mathematica, Tome 100 (1991) no. 3, pp. 219-228

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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].
DOI : 10.4064/sm-100-3-219-228

Ferdinand Beckhoff 1

1 
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Ferdinand Beckhoff. Korovkin theory in normed algebras. Studia Mathematica, Tome 100 (1991) no. 3, pp. 219-228. doi: 10.4064/sm-100-3-219-228

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