This article is cited in 2 papers

On the Stone and Bishop Appoximation Theorems

B. T. Bilalov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences

Abstract: Generalizations of the Stone–Weierstrass and Bishop approximation theorems are presented. Given an algebra, a subspace in a continuous function space coinciding with the closure of this algebra is constructed. Analogs of these results are obtained in the case where the set of functions under consideration is not an algebra, but its closure is related to some algebra.

Keywords: Stone–Weierstrass approximation theorem, Bishop approximation theorem, uniform closure of a function algebra, uniform algebra.

UDC: 517.5

Received: 15.12.2003
Revised: 05.10.2006

DOI: 10.4213/mzm3710

 English version: Mathematical Notes, 2007, 81:5, 590–595

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