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JOURNALS // Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika // Archive

Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2011 Number 1(13), Pages 44–46 (Mi vtgu172)

This article is cited in 1 paper

MATHEMATICS

On a necessary condition for a system of normalized elements to be a basis in a Hilbert space

M. A. Sadybekov, A. M. Sarsenbi

South-Kazakhstan State University

Abstract: 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, biorthogonal system, necessary condition for the basis.

UDC: 517.982


Accepted: January 10, 2011



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