Research Article

Stone-Weierstrass approximation revisited

Published in: Quaestiones Mathematicae
Volume 47 , issue sup1 , 2024 , pages: 265–281

DOI: 10.2989/16073606.2023.2287846

Author(s): Anatoly G. Kusraev Southern Mathematical Institute of the Vladikavkaz Science Center of the Russian Academy of Sciences, Russia , Semën S. Kutateladze Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Russia

Keywords: 46B04 , 46B20 , 46B42 , 46B40 , Stone-Weierstrass theorem , lattice normed space , order approximation , Boolean valued analysis , extreme operator , pure state

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Abstract

The aim of the present article is to extend the Stone-Weierstrass theorem to functions ranging in a lattice normed space and admitting order rather than topological approximation. We proceed with the machinery of Boolean-valued transfer from lattice normed space to normed space.

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