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

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Matematicheskie Zametki, 1973, Volume 14, Issue 5, Pages 723–732 (Mi mzm9957)

This article is cited in 3 scientific papers (total in 4 papers)

Certain numerical characteristics of

K N

$KN$ -lineals

Yu. A. Abramovich, G. Ya. Lozanovskii

Full-text PDF (1318 kB) Citations (4)

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

$X$ be a

K_{σ} N

$K_\sigma N$ -space or a

K B

$KB$ -lineal. If every sequence

{x_{n}} \subset X

$\{x_n\}\subset X$ of pairwise disjoint positive elements with norms not exceedings 1 we have

\underset{n \to \infty}{\lim_{_}} \frac{1}{n} | | x_{1} \lor x_{2} \lor \dots \lor x_{n} | | = 0,

$\varliminf_{n\to\infty}\frac1n||x_1\vee x_2\vee\dots\vee x_n||=0,$
then all the odd conjugate spaces

X^{*}, X^{* * *}, \dots

$X^*, X^{***},\dots$ are

K B

$KB$ -spaces.

Received: 13.09.1971

English version:
Mathematical Notes, 1973, Volume 14, Issue 5, Pages 973–978
DOI: https://doi.org/10.1007/BF01462260

Bibliographic databases:

Document Type: Article

UDC: 513.8

Language: Russian

Citation: Yu. A. Abramovich, G. Ya. Lozanovskii, “Certain numerical characteristics of

K N

$KN$ -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/mzm9957}

\mathscinet{http://mathscinet.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}

Linking options:

https://www.mathnet.ru/eng/mzm9957

https://www.mathnet.ru/eng/mzm/v14/i5/p723

This publication is cited in the following 4 articles:

Andreas Defant, Mieczysław Mastyło, “Aspects of the Kahane–Salem–Zygmund inequalities in Banach spaces”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117:1 (2023)
M. Sh. Braverman, A. A. Sedaev, “A characteristic of symmetrical spaces”, Funct. Anal. Appl., 15:2 (1981), 126–128
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
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, 33:1 (1978), 183–188

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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