Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 1, Pages 3–25 (Mi izv1379)  

This article is cited in 5 scientific papers (total in 5 papers)

Integration on Jordan algebras

Sh. A. Ayupov


Abstract: In this paper the author gives a onassociative generalization of abstract integration on JBW-algebras – Jordan Banach algebras having a predual space. Using a faithful normal finite trace on a JBW-algebra $A$, a opology of convergence in measure is introduced and the Jordan algebra $\widehat A$ of all measurable elements with respect to $A$ is constructed as the completion of $A$ in this topology. The spaces $L_1$ and $L_2$ are introduced for $A$ and it is shown that they can be considered as the spaces of all integrable and square-integrable elements, respectively, of $\widehat A$. As in the case of von Neumann algebras it is proved that $L_1$ is isometrically isomorphic to the Banach space predual to $A$.
Bibliography: 33 titles.

Full text: PDF file (1286 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1984, 22:1, 1–21

Bibliographic databases:

UDC: 517.986+517.987
MSC: Primary 17C50, 46H99, 46L05; Secondary 12J19, 46A40, 46G12
Received: 07.05.1980

Citation: Sh. A. Ayupov, “Integration on Jordan algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 47:1 (1983), 3–25; Math. USSR-Izv., 22:1 (1984), 1–21

Citation in format AMSBIB
\Bibitem{Ayu83}
\by Sh.~A.~Ayupov
\paper Integration on Jordan algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 1
\pages 3--25
\mathnet{http://mi.mathnet.ru/izv1379}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=688916}
\zmath{https://zbmath.org/?q=an:0532.46038}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 22
\issue 1
\pages 1--21
\crossref{https://doi.org/10.1070/IM1984v022n01ABEH001431}


Linking options:
  • http://mi.mathnet.ru/eng/izv1379
  • http://mi.mathnet.ru/eng/izv/v47/i1/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sh. A. Ayupov, “Locally measurable operators for $JW$-algebras and the representation of ordered Jordan algebras”, Math. USSR-Izv., 24:2 (1985), 199–220  mathnet  crossref  mathscinet  zmath
    2. N. V. Trunov, “Integration with respect to weight on $JBW$-algebras”, Funct. Anal. Appl., 19:3 (1985), 228–230  mathnet  crossref  mathscinet  zmath  isi
    3. I. G. Ganiev, A. K. Karimov, “Svoistva skhodimosti po mere na iordanovykh algebrakh”, Vladikavk. matem. zhurn., 5:4 (2003), 43–49  mathnet  mathscinet  zmath  elib
    4. M. A. Berdikulov, “Order-unit spaces which are Banach dual spaces”, Zhurn. matem. fiz., anal., geom., 2:2 (2006), 130–137  mathnet  mathscinet  zmath  elib
    5. M. A. Berdikulov, “Martingale ergodic processes in Jordan Banach algebras”, Siberian Adv. Math., 23:3 (2013), 175–179  mathnet  crossref  mathscinet  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:178
    Full text:69
    References:25
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021