Open Access

# About one class of Hilbert space uncoditional bases

### Abstract

Let a sequence $\left\{v_k \right\}^{+\infty}_{-\infty}\in l_2$ and a real sequence $\left\{\lambda_k \right\}^{+\infty}_{-\infty}$ such that $\left\{\lambda_k^{-1} \right\}^{+\infty}_{-\infty}\in l_2$, and an orthonormal basis $\left\{e_k \right\}^{+\infty}_{-\infty}$ of a Hilbert space be given. We describe a sequence $M=\left\{\mu_k \right\}^{+\infty}_{-\infty}$, $M\cap \mathbb{R}=\varnothing$, such that the families $$f_k = \sum\limits_{j\in\mathbb{Z}} {v_j\left(\lambda_j-\bar{\mu}_k \right)^{-1}}e_k, \quad k\in \mathbb{Z}$$ form an unconditional basis in $\mathfrak{H}$.

### Article Information

 Title About one class of Hilbert space uncoditional bases Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 3, 296-300 MathSciNet MR2356762 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

A. A. Tarasenko
Universidad Autonoma del Estado de Hidalgo Pachuca, Hidalgo, Mexico

M. G. Volkova
South-Ukrainian Pedagogical University, Odessa, Ukraine

### Citation Example

A. A. Tarasenko and M. G. Volkova, About one class of Hilbert space uncoditional bases, Methods Funct. Anal. Topology 13 (2007), no. 3, 296-300.

### BibTex

@article {MFAT404,
AUTHOR = {Tarasenko, A. A. and Volkova, M. G.},
TITLE = {About one class of Hilbert space uncoditional bases},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {3},
PAGES = {296-300},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=404},
}