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Mat. Sb., 2018, Volume 209, Number 10, Pages 50–70 (Mi msb8843)  

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

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8843

Full text: PDF file (663 kB)
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English version:
Sbornik: Mathematics, 2018, 209:10, 1463–1481

Bibliographic databases:

UDC: 517.98+517.982.254
MSC: Primary 46A35, 46A45; Secondary 46B70
Received: 15.10.2016 and 03.11.2017

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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\pages 50--70
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