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Sib. Èlektron. Mat. Izv., 2008, Volume 5, Pages 293–333 (Mi semr108)  

This article is cited in 10 scientific papers (total in 11 papers)

Research papers

The Wickstead Problem

A. E. Gutmana, A. G. Kusraevb, S. S. Kutateladzea

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Institute of Applied Mathematics and Informatics, Vladikavkaz, Russia

Abstract: In 1977 Anthony Wickstead raised the question of the conditions for all band preserving linear operators to be order bounded in a vector lattice. This article overviews the main ideas and results on the Wickstead problem and its variations, focusing primarily on the case of band preserving operators in a universally complete vector lattice.

Keywords: Band preserving operator, universally complete vector lattice, $\sigma$-distributive Boolean algebra, local Hamel basis, transcendence basis, derivation, Boolean valued representation.

Full text: PDF file (1177 kB)
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Bibliographic databases:
UDC: 517.98
MSC: 46A40, 47B60, 12F20, 03C90, 03C98
Received February 13, 2008, published July 1, 2008
Language:

Citation: A. E. Gutman, A. G. Kusraev, S. S. Kutateladze, “The Wickstead Problem”, Sib. Èlektron. Mat. Izv., 5 (2008), 293–333

Citation in format AMSBIB
\Bibitem{GutKusKut08}
\by A.~E.~Gutman, A.~G.~Kusraev, S.~S.~Kutateladze
\paper The Wickstead Problem
\jour Sib. \`Elektron. Mat. Izv.
\yr 2008
\vol 5
\pages 293--333
\mathnet{http://mi.mathnet.ru/semr108}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2586639}


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    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. Albeverio S., Ayupov S.A., Kudaybergenov K.K., “Structure of derivations on various algebras of measurable operators for type I von Neumann algebras”, J. Funct. Anal., 256:9 (2009), 2917–2943  crossref  mathscinet  zmath  isi  elib
    2. Toumi M.A., Toumi N., “The Wickstead problem on Dedekind sigma-complete vector lattices”, Positivity, 14:1 (2010), 135–144  crossref  mathscinet  zmath  isi
    3. Albeverio S., Ayupov Sh., Kudaybergenov K., Djumamuratov R., “Automorphisms of central extensions of type I von Neumann algebras”, Studia Math., 207:1 (2011), 1–17  crossref  mathscinet  zmath  isi  elib
    4. Albeverio S., Ayupov Sh.A., Kudaybergenov K.K., Nurjanov B.O., “Local derivations on algebras of measurable operators”, Commun. Contemp. Math., 13:4 (2011), 643–657  crossref  mathscinet  zmath  isi  elib
    5. Ayupov Sh.A., Kudaybergenov K.K., “Additive Derivations on Algebras of Measurable Operators”, J. Operat. Theor., 67:2 (2012), 495–510  mathscinet  mathscinet  zmath  isi  elib
    6. S. K. Vodopyanov, E. I. Gordon, A. E. Gutman, A. V. Koptev, S. S. Kutateladze, S. A. Malyugin, Yu. G. Reshetnyak, “Anatoliyu Georgievichu Kusraevu — 60 let”, Sib. elektron. matem. izv., 10 (2013), 13–29  mathnet
    7. G. B. Levitina, V. I. Chilin, “Derivations on ideals in commutative $AW^*$-algebras”, Siberian Adv. Math., 24:1 (2014), 26–42  mathnet  crossref  mathscinet
    8. Z. A. Kusraeva, “Nerasshiryayuschie algebraicheskie operatory”, Vladikavk. matem. zhurn., 15:3 (2013), 54–57  mathnet
    9. Sh. A. Ayupov, R. Z. Abdullaev, K. K. Kudaybergenov, “On a certain class of operator algebras and their derivations”, Eurasian Math. J., 5:1 (2014), 82–94  mathnet
    10. Zhu H., Liu Y., Xu Ya., “On Derivations of Linguistic Truth-Valued Lattice Implication Algebras”, Int. J. Mach. Learn. Cybern., 9:4 (2018), 611–620  crossref  isi  scopus
    11. A. G. Kusraev, S. S. Kutateladze, “Two applications of Boolean valued analysis”, Siberian Math. J., 60:5 (2019), 902–910  mathnet  crossref  crossref  isi  elib
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