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Mat. Zametki, 1973, Volume 14, Issue 5, Pages 723–732 (Mi mz9957)  

This article is cited in 2 scientific papers (total in 3 papers)

Certain numerical characteristics of $KN$-lineals

Yu. A. Abramovich, G. Ya. Lozanovskii


Abstract: We study the properties of certain numerical characteristics in a normed lattice that characterize its conjugate space. A typical result is as follows: let $X$ be a $K_\sigma N$-space or a $KB$-lineal. If every sequence $\{x_n\}\subset X$ of pairwise disjoint positive elements with norms not exceedings 1 we have
$$ \varliminf_{n\to\infty}\frac1n||x_1\vee x_2\vee…\vee x_n||=0, $$
then all the odd conjugate spaces $X^*, X^{***},…$ are $KB$-spaces.

Full text: PDF file (1318 kB)

English version:
Mathematical Notes, 1973, 14:5, 973–978

Bibliographic databases:

UDC: 513.8
Received: 13.09.1971

Citation: Yu. A. Abramovich, G. Ya. Lozanovskii, “Certain numerical characteristics of $KN$-lineals”, Mat. Zametki, 14:5 (1973), 723–732; Math. Notes, 14:5 (1973), 973–978

Citation in format AMSBIB
\Bibitem{AbrLoz73}
\by Yu.~A.~Abramovich, G.~Ya.~Lozanovskii
\paper Certain numerical characteristics of $KN$-lineals
\jour Mat. Zametki
\yr 1973
\vol 14
\issue 5
\pages 723--732
\mathnet{http://mi.mathnet.ru/mz9957}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=338727}
\zmath{https://zbmath.org/?q=an:0287.46010}
\transl
\jour Math. Notes
\yr 1973
\vol 14
\issue 5
\pages 973--978
\crossref{https://doi.org/10.1007/BF01462260}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Bukhvalov, A. I. Veksler, D. A. Vladimirov, B. Z. Vulikh, L. V. Kantorovich, S. M. Lozinskii, E. M. Semenov, “Grigorii Yakovlevich Lozanovskii (obituary)”, Russian Math. Surveys, 3:1 (1978), 183–188  mathnet  crossref  mathscinet  zmath
    2. A. V. Bukhvalov, A. I. Veksler, G. Ya. Lozanovskii, “Banach lattices – some Banach aspects of their theory”, Russian Math. Surveys, 34:2 (1979), 159–212  mathnet  crossref  mathscinet  zmath
    3. M. Sh. Braverman, A. A. Sedaev, “A characteristic of symmetrical spaces”, Funct. Anal. Appl., 15:2 (1981), 126–128  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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