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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)
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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
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 10, Pages 50–70
DOI: https://doi.org/10.4213/sm8843
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 $(d_1)$”, Mat. Sb., 209:10 (2018), 50–70; Sb. Math., 209:10 (2018), 1463–1481
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:57
    First page:29
     
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