On the existence of a basis in a complemented subspace of a nuclear Köthe space of type $d_2$
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 9-20
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The existence of a basis in a complemented subspace of a nuclear Köthe 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.
@article{VMJ_2016_18_1_a1,
     author = {A. K. Dronov},
     title = {On the existence of a~basis in a~complemented subspace of a~nuclear {K\"othe} space of type~$d_2$},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {9--20},
     year = {2016},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a1/}
}
TY  - JOUR
AU  - A. K. Dronov
TI  - On the existence of a basis in a complemented subspace of a nuclear Köthe space of type $d_2$
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 9
EP  - 20
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a1/
LA  - ru
ID  - VMJ_2016_18_1_a1
ER  - 
%0 Journal Article
%A A. K. Dronov
%T On the existence of a basis in a complemented subspace of a nuclear Köthe space of type $d_2$
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 9-20
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a1/
%G ru
%F VMJ_2016_18_1_a1
A. K. Dronov. On the existence of a basis in a complemented subspace of a nuclear Köthe space of type $d_2$. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 9-20. http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a1/

[1] Berg I., Lefstrem I., Interpolyatsionnye prostranstva, Mir, M., 1980, 264 pp. | MR

[2] Vulikh B. Z., Vvedenie v teoriyu poluuporyadochennykh prostranstv, Gos. izd-vo fiz.-mat. lit-ry, M., 1961, 407 pp. | MR

[3] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh samosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965, 448 pp. | MR

[4] Dragilev M. M., Bazisy v prostranstvakh Këte, Izd-vo RGU, Rostov-n/D, 1983, 144 pp.

[5] Kaplitskii V. M., Dronov A. K., “K teorii interpolyatsii operatorov, ogranichennykh na konusakh v vesovykh prostranstvakh chislovykh posledovatelnostei”, Zapiski nauchnykh seminarov POMI, 424, 2014, 154–178

[6] Kondakov V. P., Voprosy geometrii nenormiruemykh prostranstv, Izd-vo RGU, Rostov-n/D, 1983, 72 pp. | MR

[7] Kondakov V. P., “Ob operatorakh i dopolnyaemykh podprostranstvakh v prostranstvakh Këte, opredelyaemykh razryazhënnymi matritsami”, Sib. mat. zhurn., 36:5 (1995), 1096–1112 | MR | Zbl

[8] Kondakov V. P., “Geometricheskie svoistva prostranstv Freshe i vydelenie bazisnykh posledovatelnostei”, Mat. zametki, 66:1 (1999), 102–111 | DOI | MR | Zbl

[9] Kondakov V. P., “Zamechanie o suschestvovanii bazisov v vesovykh schetno-gilbertovykh prostranstvakh i ikh dopolnyaemykh podprostranstvakh”, Sib. mat. zhurn., 43:6 (2001), 1300–1313 | MR | Zbl

[10] Kondakov V. P., Efimov A. I., “O klassakh prostranstv Këte, v kotorykh kazhdoe dopolnyaemoe podprostranstvo imeet bazis”, Vladikavk. mat. zhurn., 10:2 (2008), 21–29 | MR | Zbl

[11] Krein M. G., “O minimalnom razlozhenii funktsionala na polozhitelnye sostavlyayuschie”, Dokl. AN SSSR, 28:1 (1940), 18–22 | MR | Zbl

[12] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR

[13] Mityagin B. S., Khenkin G. M., “Lineinye zadachi kompleksnogo analiza”, Uspekhi mat. nauk, 26:4 (1970), 93–152 | MR | Zbl

[14] Peetre J., “On interpolation functions. III”, Acta Sci. Math., 30:3–4 (1969), 235–239 | MR | Zbl

[15] Pelczynski A., “Problem 37”, Stud. Math., 38 (1970), 18–22 | MR

[16] Pich A., Yadernye lokalno vypuklye prostranstva, Mir, M., 1970 | MR

[17] Vogt D., “Ein Isomorphiesatz für Potenzreihenräume”, Arch. Match., 38 (1982), 540–548 | DOI | MR | Zbl