The Kaplan extension of the ring and Banach algebra of continuous functions as a divisible hull

V. K. Zakharov


Abstract: The new algebraic structure of $c$-rings and $c$-algebras with a refinement is introduced, and on its basis the concept of a divisible hull of graduated type. These concepts are used to obtain a ring and Banach algebra characterization of the universally measurable extension $C\rightarrowtail UM$ as a certain type of divisible hull of the ring and Banach algebra $C$ of all bounded continuous functions on an Aleksandrov space (Theorem 1). For purposes of comparison a description of the Arens second dual extension $C\rightarrowtail C''$ is given without proof (Theorem 2).

UDC: 512.552

MSC: Primary 46E25, 54D35, 54C40; Secondary 46J10, 46E30

Received: 29.09.1992

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1995, 45:3, 477–493

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