Geodesic
On some systems of a~Hilbert space which are not bases
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2010), pp. 53-60

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In this paper we consider a sequence of normalized vectors $\{h_n\}^\infty_{n=1}$ in a Hilbert space $H$ such that the inner products $\langle h_i,h_j\rangle\ge\alpha$, $\alpha>0$, $i\ne j$, $i,j\in\mathbf N$. It is shown that this sequence of vectors is not a base in $H$.
Keywords: Hilbert space, inner product, basis, complete sequences, angle between elements of a sequence. 
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     author = {T. E. Khmyleva and O. G. Ivanova},
     title = {On some systems of {a~Hilbert} space which are not bases},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {53--60},
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T. E. Khmyleva; O. G. Ivanova. On some systems of a~Hilbert space which are not bases. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 3 (2010), pp. 53-60. http://geodesic.mathdoc.fr/item/VTGU_2010_3_a6/