Lebesgue constants for Chebyshev thresholding greedy algorithms - Shao, Chunfang; Ye, Peixin (Journal of inequalities and applications, 2018)
We investigate the efficiency of Chebyshev Thresholding Greedy Algorithm (CTGA) for an n -term approximation with respect to general bases in a Banach space. We show that the convergence property of CTGA is better than TGA for non-quasi-greedy bases. Then we determine the exact rate of the Lebesgue constants L n ch for two examples of such bases: the trigonometric system and the summing basis. We also establish the upper estimates for L n ch with respect to general bases in terms of quasi-greedy parameter, democracy parameter and A-property parameter. These estimates do not involve an unconditionality parameter, therefore they are better than those of TGA. In particular, for conditional quasi-greedy bases, a faster convergence rate is obtained.