Abstract:
We give versions of a criterion for existence of unconditional bases for countably-Hilbert spaces. As applications we obtain theorems on existence of unconditional bases for certain classes of countably-Hilbert function spaces and for their complemented subspaces under additional constraints on the space and the corresponding projections to the complemented subspaces. These classes include generalizations of power series spaces of finite type and Kothe spaces determined by Dragilev-type functions.
Citation:
V. P. Kondakov, “Remarks on the existence of unconditional bases for weighted countably-Hilbert spaces and their complemented subspaces”, Sibirsk. Mat. Zh., 42:6 (2001), 1300–1313; Siberian Math. J., 42:6 (2001), 1082–1092
\Bibitem{Kon01}
\by V.~P.~Kondakov
\paper Remarks on the existence of unconditional bases for weighted countably-Hilbert spaces and their complemented subspaces
\jour Sibirsk. Mat. Zh.
\yr 2001
\vol 42
\issue 6
\pages 1300--1313
\mathnet{http://mi.mathnet.ru/smj1387}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1876816}
\zmath{https://zbmath.org/?q=an:0986.46002}
\transl
\jour Siberian Math. J.
\yr 2001
\vol 42
\issue 6
\pages 1082--1092
\crossref{https://doi.org/10.1023/A:1012840509978}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000172981200006}
Linking options:
https://www.mathnet.ru/eng/smj1387
https://www.mathnet.ru/eng/smj/v42/i6/p1300
This publication is cited in the following 7 articles:
A. K. Dronov, V. M. Kaplitskii, “On the existence of a basis in a complemented subspace of a nuclear Köthe space from class (d1)”, Sb. Math., 209:10 (2018), 1463–1481
A. K. Dronov, “O suschestvovanii bazisa v dopolnyaemom podprostranstve yadernogo prostranstva Këte iz klassa (d2)”, Vladikavk. matem. zhurn., 18:1 (2016), 9–20
Faried N., El-Sharkawy H.A., “Fixed Points in Countably Hilbert Spaces”, J. Inequal. Appl., 2016, 26
N. T. Akhtyamov, I. Kh. Musin, “O suschestvovanii bazisa v vesovom prostranstve tselykh funktsii”, Ufimsk. matem. zhurn., 1:1 (2009), 3–15
V. P. Kondakov, “Kharakterizatsiya dopolnyaemykh podprostranstv v dekartovykh proizvedeniyakh strukturno nesravnimykh prostranstv Këte iz klassov (f)0 i (f)1 Dragileva”, Vladikavk. matem. zhurn., 6:2 (2004), 17–20
V. P. Kondakov, “On complemented subspaces of some Köthe spaces of infinite type”, Siberian Math. J., 44:1 (2003), 93–98
V. P. Kondakov, A. I. Efimov, “O dvukh klassakh prostranstv Këte — Freshe, v kotorykh kazhdoe dopolnyaemoe podprostranstvo imeet bazis”, Vladikavk. matem. zhurn., 5:4 (2003), 50–62
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