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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 5, Pages 1105–1114 (Mi izv2577)  

This article is cited in 5 scientific papers (total in 5 papers)

A geometrical conjecture of Banach

M. L. Gromov


Abstract: This article is devoted to the following problem of Banach: Let $B^n$ be a Banach space of finite or infinite dimension $n$ and let $k$ be a natural number satisfying the inequalities $1<k<n$; if all the $k$-dimensional subspaces of $B^n$ are isometric to each other, is $B^n$ a Hilbert space? We give a positive answer to this question under certain restrictions on $k$ and $n$.

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:5, 1055–1064

Bibliographic databases:

UDC: 513.8
MSC: 46B04, 46Cxx, 22Exx
Received: 14.09.1966

Citation: M. L. Gromov, “A geometrical conjecture of Banach”, Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967), 1105–1114; Math. USSR-Izv., 1:5 (1967), 1055–1064

Citation in format AMSBIB
\Bibitem{Gro67}
\by M.~L.~Gromov
\paper A geometrical conjecture of Banach
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 5
\pages 1105--1114
\mathnet{http://mi.mathnet.ru/izv2577}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=217566}
\zmath{https://zbmath.org/?q=an:0162.44402|0176.10903}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 5
\pages 1055--1064
\crossref{https://doi.org/10.1070/IM1967v001n05ABEH000599}


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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. V. D. Milman, “Geometric theory of Banach spaces. Part II. Geometry of the unit sphere”, Russian Math. Surveys, 26:6 (1971), 79–163  mathnet  crossref  mathscinet  zmath
    2. A. Pełczyński, “On some problems of Banach”, Russian Math. Surveys, 28:5 (1973), 67–76  mathnet  crossref  mathscinet  zmath
    3. Emeric Deutsch, Hans Schneider, “Bounded groups and norm-Hermitian matrices”, Linear Algebra and its Applications, 9 (1974), 9  crossref
    4. Jon Aaronson, Eli Glasner, Michal Misiurewicz, “Rigid sets in the plane”, Isr J Math, 68:3 (1989), 307  crossref  mathscinet  zmath  isi
    5. R. N. Karasev, “Topological methods in combinatorial geometry”, Russian Math. Surveys, 63:6 (2008), 1031–1078  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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