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 $\mathfrak{H}$.

Full Text

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},
  MRNUMBER = {MR2356762},
       URL = {http://mfat.imath.kiev.ua/article/?id=404},
}