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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).
Received: 29.09.1992
Citation:
V. K. Zakharov, “The Kaplan extension of the ring and Banach algebra of continuous functions as a divisible hull”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 477–493
Linking options:
https://www.mathnet.ru/eng/im523https://doi.org/10.1070/IM1995v045n03ABEH001669 https://www.mathnet.ru/eng/im/v58/i6/p51
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