Approximation of infinite matrices by matricial Haar polynomials

Sorina Barza Department of Engineering Sciences Physics and Mathematics, Karlstad University Victor Lie Institute of Mathematics of Romanian Academy, P. O. Box 1-764, Bucharest, Romania Nicolae Popa Institute of Mathematics of Romanian Academy, P. O. Box 1-764, Bucharest, Romania

TBD mathscidoc:1701.333056

Arkiv for Matematik, 43, (2), 251-269, 2003.12
The main goal of this paper is to extend the approximation theorem of contiuous functions by Haar polynomials (see Theorem A) to infinite matrices (see Theorem C). The extension to the matricial framework will be based on the one hand on the remark that periodic functions which belong to$L$^{∞}($T$) may be one-to-one identified with Toeplitz matrices from$B$($l$_{2}) (see Theorem 0) and on the other hand on some notions given in the paper. We mention for instance:$ms$—a unital commutative subalgebra of$l$^{∞},$C$($l$_{2}) the matricial analogue of the space of all continuous periodic functions$C$($T$), the matricial Haar polynomials, etc.
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@inproceedings{sorina2003approximation,
  title={Approximation of infinite matrices by matricial Haar polynomials},
  author={Sorina Barza, Victor Lie, and Nicolae Popa},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203614218650865},
  booktitle={Arkiv for Matematik},
  volume={43},
  number={2},
  pages={251-269},
  year={2003},
}
Sorina Barza, Victor Lie, and Nicolae Popa. Approximation of infinite matrices by matricial Haar polynomials. 2003. Vol. 43. In Arkiv for Matematik. pp.251-269. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203614218650865.
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