Vladikavkazskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vladikavkaz. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






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


Vladikavkaz. Mat. Zh., 2017, Volume 19, Number 3, Pages 41–50 (Mi vmj623)  

This article is cited in 1 scientific paper (total in 1 paper)

Maximal quasi-normed extension of quasi-normed lattices

A. G. Kusraevab, B. B. Tasoevc

a North Ossetian State University, 44-46 Vatutin Street, Vladikavkaz, 362025, Russia
b Vladikavkaz Science Center of the RAS, 22 Markus Street, Vladikavkaz, 362027, Russia
c Southern Mathematical Institute — the Affiliate of Vladikavkaz Science Center of the RAS, 22 Markus street, Vladikavkaz, 362027, Russia

Abstract: The purpose of this article is to extend the Abramovich's construction of a maximal normed extension of a normed lattice to quasi-Banach setting. It is proved that the maximal quasi-normed extension $X^\varkappa$ of a Dedekind complete quasi-normed lattice $X$ with the weak $\sigma$-Fatou property is a quasi-Banach lattice if and only if $X$ is intervally complete. Moreover, $X^\varkappa$ has the Fatou and the Levi property provided that $X$ is a Dedekind complete quasi-normed space with the Fatou property. The possibility of applying this construction to the definition of a space of weakly integrable functions with respect to a measure taking values from a quasi-Banach lattice is also discussed, since the duality based definition does not work in the quasi-Banach setting.

Key words: quasi-Banach lattice, maximal quasi-normed extension, Fatou property, Levi property vector measure, space of weakly integrable functions.

Full text: PDF file (266 kB)
References: PDF file   HTML file
UDC: 517.98
MSC: 46A16, 46B42, 46E30, 46G10, 47B38, 47G10
Received: 14.07.2017
Language:

Citation: A. G. Kusraev, B. B. Tasoev, “Maximal quasi-normed extension of quasi-normed lattices”, Vladikavkaz. Mat. Zh., 19:3 (2017), 41–50

Citation in format AMSBIB
\Bibitem{KusTas17}
\by A.~G.~Kusraev, B.~B.~Tasoev
\paper Maximal quasi-normed extension of quasi-normed lattices
\jour Vladikavkaz. Mat. Zh.
\yr 2017
\vol 19
\issue 3
\pages 41--50
\mathnet{http://mi.mathnet.ru/vmj623}


Linking options:
  • http://mi.mathnet.ru/eng/vmj623
  • http://mi.mathnet.ru/eng/vmj/v19/i3/p41

    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. A. G. Kusraev, B. B. Tasoev, “Integrirovanie po polozhitelnoi mere so znacheniyami v kvazibanakhovoi reshetke”, Vladikavk. matem. zhurn., 20:1 (2018), 69–85  mathnet  crossref  elib
  • Владикавказский математический журнал
    Number of views:
    This page:124
    Full text:46
    References:29

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