Arkiv för Matematik

  • Ark. Mat.
  • Volume 43, Number 2 (2005), 251-269.

Approximation of infinite matrices by matricial Haar polynomials

Sorina Barza, Victor Lie, and Nicolae Popa

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Abstract

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(l2) (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(l2) the matricial analogue of the space of all continuous periodic functions C(T), the matricial Haar polynomials, etc.

In Section 1 we present some results concerning the space ms—a concept important for this generalization, the proof of the main theorem being given in the second section.

Note

Partially supported by EUROMMAT ICA1-CT-2000-70022.

Note

Partially supported by V-Stabi-RUM/1022123.

Note

Partially supported by EUROMMAT ICA1-CT-2000-70022 and V-Stabi-RUM/1022123.

Article information

Source
Ark. Mat., Volume 43, Number 2 (2005), 251-269.

Dates
Received: 2 December 2003
Revised: 26 August 2004
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898899

Digital Object Identifier
doi:10.1007/BF02384779

Mathematical Reviews number (MathSciNet)
MR2173951

Zentralblatt MATH identifier
1097.15022

Rights
2005 © Institut Mittag-Leffler

Citation

Barza, Sorina; Lie, Victor; Popa, Nicolae. Approximation of infinite matrices by matricial Haar polynomials. Ark. Mat. 43 (2005), no. 2, 251--269. doi:10.1007/BF02384779. https://projecteuclid.org/euclid.afm/1485898899


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References

  • [AJPR] Aleksandrov, A. B., Janson, S., Peller, V. V., and Rochberg, R., Function Spaces, Interpolation Theory and Related Topics (Lund, 2000), pp. 61–149, de Gruyter, Berlin 2002.
  • [BPP] Barza, S., Persson, L.-E. and Popa, N., A matriceal analogue of Fejér's theory, Math. Nachr. 260 (2003), 14–20.
  • [B] Bennett, G., Schur multipliers, Duke Math. J. 44 (1977), 603–639.
  • [KS] Kaczmarz, S. and Steinhaus, H., Theorie der orthogonal Reihen, Subwencji Funduszu Kultury Narodowes, Warsaw-Lwow, 1935.
  • [K] Katznelson, Y., An Introduction to Harmonic Analysis, Wiley, New York, 1968.
  • [Zh] Zhu K. H., Operator Theory in Function Spaces, Marcel Dekker, New York, 1990.
  • [Zy] Zygmund, A., Trigonometric Series, I–II, Cambridge Univ. Press, Cambridge, 1959.