Geodesic
On a~necessary condition for a~system of normalized elements to be a~basis in a~Hilbert space
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2011), pp. 44-46

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider a complete, minimal, almost normalized sequence $\{\varphi_k\}^\infty_{k=1}$ of elements of a Hilbert space $H$ such that their inner products have the property $|(\varphi_k,\varphi_j)|\ge\alpha$, $\alpha>0$ for all sufficiently large numbers $k,j$. It was proved that this sequence is not an unconditional basis in $H$.
Keywords: Hilbert space, almost normalized sequence, unconditional basis, Riesz basis, necessary condition for the basis.
Mots-clés : biorthogonal system 
@article{VTGU_2011_1_a4,
     author = {M. A. Sadybekov and A. M. Sarsenbi},
     title = {On a~necessary condition for a~system of normalized elements to be a~basis in {a~Hilbert} space},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {44--46},
     publisher = {mathdoc},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2011_1_a4/}
}
TY  - JOUR
AU  - M. A. Sadybekov
AU  - A. M. Sarsenbi
TI  - On a~necessary condition for a~system of normalized elements to be a~basis in a~Hilbert space
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2011
SP  - 44
EP  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTGU_2011_1_a4/
LA  - ru
ID  - VTGU_2011_1_a4
ER  - 
%0 Journal Article
%A M. A. Sadybekov
%A A. M. Sarsenbi
%T On a~necessary condition for a~system of normalized elements to be a~basis in a~Hilbert space
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2011
%P 44-46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTGU_2011_1_a4/
%G ru
%F VTGU_2011_1_a4
M. A. Sadybekov; A. M. Sarsenbi. On a~necessary condition for a~system of normalized elements to be a~basis in a~Hilbert space. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 1 (2011), pp. 44-46. http://geodesic.mathdoc.fr/item/VTGU_2011_1_a4/