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About one class of Hilbert space uncoditional bases

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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 $\mathfrak{H}$.


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Article Information

TitleAbout one class of Hilbert space uncoditional bases
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 3, 296-300
MathSciNet MR2356762
CopyrightThe 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},
}


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