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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}
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