Lebesgue constants for Chebyshev thresholding greedy algorithms

Abstract 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 Lnch $L_{n}^{\mathrm{ch}}$ for two examples of such bases: the trigonometric system and the summing basis. We also establish the upper estimates for Lnch $L_{n}^{\mathrm{ch}}$ 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.

Abstract licence: CC BY-NC-ND

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