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Izv. RAN. Ser. Mat., 1994, Volume 58, Issue 6, Pages 51–68 (Mi izv523)  

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).

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

Bibliographic databases:

UDC: 512.552
MSC: Primary 46E25, 54D35, 54C40; Secondary 46J10, 46E30
Received: 29.09.1992

Citation: V. K. Zakharov, “The Kaplan extension of the ring and Banach algebra of continuous functions as a divisible hull”, Izv. RAN. Ser. Mat., 58:6 (1994), 51–68; Russian Acad. Sci. Izv. Math., 45:3 (1995), 477–493

Citation in format AMSBIB
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\by V.~K.~Zakharov
\paper The Kaplan extension of the ring and Banach algebra of continuous functions as a~divisible hull
\jour Izv. RAN. Ser. Mat.
\yr 1994
\vol 58
\issue 6
\pages 51--68
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1317208}
\zmath{https://zbmath.org/?q=an:0878.46040}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 45
\issue 3
\pages 477--493
\crossref{https://doi.org/10.1070/IM1995v045n03ABEH001669}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995TW91000002}


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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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