Article

# Trigonometric bases for matrix weighted Lp-spaces

Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg East, Denmark
Journal of Mathematical Analysis and Applications DOI:10.1016/j.jmaa.2010.06.015 pp.784-792

ABSTRACT We give a complete characterization of 2π-periodic matrix weights W for which the vector-valued trigonometric system forms a Schauder basis for the matrix weighted space Lp(T;W). Then trigonometric quasi-greedy bases for Lp(T;W) are considered. Quasi-greedy bases are systems for which the simple thresholding approximation algorithm converges in norm. It is proved that such a trigonometric basis can be quasi-greedy only for p=2, and whenever the system forms a quasi-greedy basis, the basis must actually be a Riesz basis.

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### Keywords

2π-periodic matrix weights W

complete characterization

Quasi-greedy bases

simple thresholding approximation algorithm converges

system forms

trigonometric quasi-greedy bases

vector-valued trigonometric system forms