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Sbornik: Mathematics, 2018, Volume 209, Issue 10, Pages 1463–1481
DOI: https://doi.org/10.1070/SM8843 (Mi sm8843) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the existence of a basis in a complemented subspace of a nuclear Köthe space from class $(d_1)$

A. K. Dronova, V. M. Kaplitskiibc

a Rostov State University of Economics, Rostov-on-Don
b Southern Federal University, Rostov-on-Don
c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
English version PDF (508 kB) Citations (1) Russian version article
References:
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DOI: https://doi.org/10.1070/SM8843
Abstract: A proof is presented that an arbitrary complemented subspace of a Köthe nuclear space from class $(d_1)$ has a basis, provided that the relevant Köthe matrix is regular in the sense of Dragilev. It is also shown that each such subspace must have a basis that is quasi-equivalent to a part of the canonical unit-vector basis.
Bibliography: 21 titles.
Keywords: basis, Köthe nuclear spaces, Pelczyński's conjecture, complemented subspaces.
Received: 15.10.2016 and 03.11.2017
Bibliographic databases:
Document Type: Article
UDC: 517.98+517.982.254
MSC: Primary 46A35, 46A45; Secondary 46B70
Language: English
Original paper language: Russian
Citation: A. K. Dronov, V. M. Kaplitskii, “On the existence of a basis in a complemented subspace of a nuclear Köthe space from class $(d_1)$”, Sb. Math., 209:10 (2018), 1463–1481
Citation in format AMSBIB
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\by A.~K.~Dronov, V.~M.~Kaplitskii
\paper On the existence of a~basis in a~complemented subspace of a~nuclear K\"othe space from class~$(d_1)$
\jour Sb. Math.
\yr 2018
\vol 209
\issue 10
\pages 1463--1481
\mathnet{http://mi.mathnet.ru/eng/sm8843}
\crossref{https://doi.org/10.1070/SM8843}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3859409}
\zmath{https://zbmath.org/?q=an:1425.46003}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059198218}
Linking options:
  • https://www.mathnet.ru/eng/sm8843
  • https://doi.org/10.1070/SM8843
  • https://www.mathnet.ru/eng/sm/v209/i10/p50
    • This publication is cited in the following 1 articles:
    1. A. Debrouwere, “Sequence space representations for spaces of entire functions with rapid decay on strips”, J. Math. Anal. Appl., 497:1 (2021), 124872  crossref  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:872
    Russian version PDF:58
    English version PDF:36
    References:75
    First page:29
     
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