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ArticleOriginal scientific text

Title

Korovkin theory in normed algebras

Authors 1

Affiliations

  1. Mathematisches Institut, Universität Münster, Einsteinstraße 62, 4400 Münster, Germany

Abstract

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].

Bibliography

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Studia Mathematica
1991/100/3
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Pages:
219-228
Main language of publication
English
Received
1990-05-28
Accepted
1991-04-25
Published
1991
Exact and natural sciences