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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 
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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/

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