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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

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},
}