RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Fundam. Prikl. Mat., 1995, Volume 1, Issue 1, Pages 221–228 (Mi fpm52)  

Locally convex modules

Z. S. Lipkina

Moscow State University of Railway Communications

Abstract: Let $K$ be a non-archimedean valued field, $A\subseteq K$ be its integer ring. This paper is devoted to the study of the locally convex topological unital $A$-modules. These modules are very close to the vector spaces over non-archimedean valued fields. In particular, the topology of these modules can be determined by some system $\Gamma$ of semipseudonorms. Monna demonstrated that $p$-adic analogue of Hahn–Banach theorem can be proved for the locally convex vector spaces over non-archimedean valued fields. One can give the definitions of $q$-injectivity, where $q$ is the seminorm which is determined on this module, and of the strong topological injectivity. It means that any $q$-bounded homomorphism can be extended with the same seminorm, where $q$ is a some fixed seminorm in the first case, and an arbitrary seminorm $q\in\Gamma$ in the second one. The necessary and sufficient conditions of $q$-injectivity and strong topological injectivity for torsion free modules are given. At last, the necessary and sufficient conditions for topological injectivity of a locally convex $A$-module in the case when $A$ is the integer ring of the main local compact non-archimedean valued field are the following ones: a topological module is complete and Baire condition holds for any continuous homomorphism (here topological injectivity means that any continuous homomorphism of a submodule can be extended to a continuous homomorphism of the whole module).

Full text: PDF file (423 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 512.55
Received: 01.02.1994

Citation: Z. S. Lipkina, “Locally convex modules”, Fundam. Prikl. Mat., 1:1 (1995), 221–228

Citation in format AMSBIB
\Bibitem{Lip95}
\by Z.~S.~Lipkina
\paper Locally convex modules
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 1
\pages 221--228
\mathnet{http://mi.mathnet.ru/fpm52}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1789361}
\zmath{https://zbmath.org/?q=an:0870.16025}


Linking options:
  • http://mi.mathnet.ru/eng/fpm52
  • http://mi.mathnet.ru/eng/fpm/v1/i1/p221

    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
  • Фундаментальная и прикладная математика
    Number of views:
    This page:180
    Full text:65
    References:22
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020