This article is cited in 2 papers

MATHEMATICS

On some systems of a Hilbert space which are not bases

T. E. Khmyleva, O. G. Ivanova

Tomsk State University, Faculty of Mechanics and Mathematics

Abstract: 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.

UDC: 517.982


Accepted: June 23, 2010