Arkiv för Matematik
- Ark. Mat.
- Volume 43, Number 2 (2005), 251-269.
Approximation of infinite matrices by matricial Haar polynomials
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.
Partially supported by EUROMMAT ICA1-CT-2000-70022.
Partially supported by V-Stabi-RUM/1022123.
Partially supported by EUROMMAT ICA1-CT-2000-70022 and V-Stabi-RUM/1022123.
Ark. Mat., Volume 43, Number 2 (2005), 251-269.
Received: 2 December 2003
Revised: 26 August 2004
First available in Project Euclid: 31 January 2017
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2005 © Institut Mittag-Leffler
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