Zapiski Nauchnykh Seminarov LOMI
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



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






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


Zapiski Nauchnykh Seminarov LOMI, 1977, Volume 73, Pages 91–101 (Mi znsl1946)  

Isomorphisms and projections for quotient-spaces of $\mathscr L_1$-spaces by their reflexive subspaces

S. V. Kislyakov
Abstract: Let $Z_1=X_1/E_1$ and $Z_2=X_2/E_2$, where $X_1$ and $X_2$ are $\mathscr L_1$-spaces $E_1\subset X_1$, $E_2\subset X_2$. In this paper we study the following questions: 1) under what conditions are $Z_1$ and $Z_2$ isomorphic; 2) under what conditions is $Z_1$ isomorphic to a complemented subspace of $Z_2$. Some results: (a) if $E_1$ and $E_2$ are reflexive and $Z_1$. is isomorphic to $Z_2$, then one of the spaces E1 E2 is isomorphic to the product of the other by a finite-dimensional space; (b) if $X_1=C(\mathbf T)^*$ ($\mathbf T$ is a circle), $E_1=H^1$ and $E_2$ is reflexive and $X_2=Y^*$ for some $Y$, then it is impossible to imbed $Z_1$ in $Z_2$ as a complemented subspace.
English version:
Journal of Soviet Mathematics, 1986, Volume 34, Issue 6, Pages 2074–2080
DOI: https://doi.org/10.1007/BF01741581
Bibliographic databases:
UDC: 513.881
Language: Russian
Citation: S. V. Kislyakov, “Isomorphisms and projections for quotient-spaces of $\mathscr L_1$-spaces by their reflexive subspaces”, Investigations on linear operators and function theory. Part VIII, Zap. Nauchn. Sem. LOMI, 73, "Nauka", Leningrad. Otdel., Leningrad, 1977, 91–101; J. Soviet Math., 34:6 (1986), 2074–2080
Citation in format AMSBIB
\Bibitem{Kis77}
\by S.~V.~Kislyakov
\paper Isomorphisms and projections for quotient-spaces of $\mathscr L_1$-spaces by their reflexive subspaces
\inbook Investigations on linear operators and function theory. Part~VIII
\serial Zap. Nauchn. Sem. LOMI
\yr 1977
\vol 73
\pages 91--101
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1946}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=513170}
\zmath{https://zbmath.org/?q=an:0596.46009 | 0406.46012}
\transl
\jour J. Soviet Math.
\yr 1986
\vol 34
\issue 6
\pages 2074--2080
\crossref{https://doi.org/10.1007/BF01741581}
Linking options:
  • https://www.mathnet.ru/eng/znsl1946
  • https://www.mathnet.ru/eng/znsl/v73/p91
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
    Statistics & downloads:
    Abstract page:261
    Full-text PDF :115
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024