Address: Vatutina st. 53, Vladikavkaz,
362025, RNO-A, Russia
Phone: (8672)23-00-54
E-mail: rio@smath.ru
DOI: 10.23671/VNC.2016.1.5927
On the Existence of a Basis in a Complemented Subspace of a Nuclear Kothe Space of Type \(d_2\)
Dronov A. K.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 1.
Abstract: The existence of a basis in a complemented subspace of a nuclear Kothe space of the class \(d_2\) is proved. It is also shown that in each such subspace there is a basis quasiequivalent to the part of the basis of orts.
For citation: Dronov A. K. On the Existence of a Basis in a Complemented Subspace of a Nuclear Kothe Space of Type \(d_2\) // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 1, pp. 9-20.
DOI 10.23671/VNC.2016.1.5927
1. Bergh J., Löfström J. Interpolation spaces. Springer, Berlin, 1976.
2. Vulih B. Z. Vvedenie v teoriyu poluuporyadochennyh prostranstv[Theory of semi-ordered spaces].
M., Gosudarstvennoe izdatel'stvo fiziko-matematicheskoj literatury, 1961 [in Russian].
3. Gohberg I.C., Kreïn M.G. Theory of Linear Nonselfadjoint Operators. Providence, R.I. :
American Math. Soc., vol. 18, 1969.
4. Dragilev M. M. Bazisy v prostranstvah Kyote [Bases in the Köthe Spaces].
Rostov-na-Donu, RGU, 1983, 144 p.
5. Kaplitskii V. M., Dronov A. K.To the Theory of Operators that are Bounded
on Cones in Weighted Spaces of Numerical Sequences. J. of Math. Sciences,
2015, vol. 209, no. 5, pp. 761-777.
6. Kondakov V. P. Voprosy geometrii nenormiruemyh prostranstv [Issues of Geometry
of Nonnormed Spaces]. Izdatel'stvo Rostovskogo Universiteta, 1983 [in Russian].
7. Kondakov V. P. On Operators and Complimented Subspaces in the Köthe Spaces Determined
by Sparse Matrices. J. of Math. Sci., 1995, vol. 36, no. 5, pp. 943-957.
8. Kondakov V. P. Geometric Properties of Fréchet Spaces and selection of basis sequences.
Math. Notes, 1999, vol. 66, no. 1, pp. 82-88.
9. Kondakov V. P. Remarks on the Existence of Unconditional Bases for Weighted
Countably-Hilbert Spaces and Their Complemented Subspaces.
Siberian Math. J., 2001, vol. 42, no. 6, pp. 1082-1092.
10. Kondakov V. P., Efimov A. I., O klassah prostranstv Kyote, v kotoryh kazhdoe
dopolnyaemoe podprostranstvo imeet bazis [On Classes of Köthe Spaces with
a basis any complemented subspace]. Vladikavkazskij Matem. Zhurnal [Vladikavkaz Math. J.],
2008, vol.10, no. 2, pp. 21-29 [in Russian].
11. Krejn M. G. O minimal'nom razlozhenii funkcionala na polozhitel'nye sostavlyayushchie
[On the Minimal Decomposition of Functional on Positive Compomemts]. DAN SSSR, 1940,
vol. 28, no. 1, pp. 18-22 [in Russian].
12. Kreïn S. G., Petunin Ju. L., Semenov E. M. Interpolation of Linear Operators.
American Math. Soc., 1983, vol. 54.
13. Mityagin B. S., Khenkin G. M. Linear Problems of Complex Analysis. Russian Math. Surveys, 1970,
vol. 26, no. 4.
14. Peetre J., On interpolation functions III. Acta Sci. Math., 1969, vol. 30, no. 3, 4, pp. 235-239.
15. Pelczynski A., Problem 37. Studia Math., 1970, vol. 38, pp. 18-22.
16. Pietsch A. Nuclear Locally Convex Spaces. Springer-Verland, 1972.
17. Vogt D. Ein Isomorphiesatz für Potenzreihenraume. Arch. Match., 1982, vol. 38, pp.540-548.
The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses.
Сайт использует файлы cookie, необходимые для корректной работы сайта, и сервисы Яндекс-метрики, используемые для анализа статистики посещаемости, которые не содержат сведений, на основании которых можно идентифицировать личность пользователя. Продолжение пользования сайтом является согласием на применение данных технологий.