KOROVKIN THEORY IN NORMED ALGEBRAS

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 union {t* o t\ t is-an-element-of 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].