Some new conditions that arise naturally in the study of the Thresholding Greedy Algorithm
are introduced for bases of8 anach spaces. We relate these conditions to best n-term …

We present various estimates for the Lebesgue type inequalities associated with the
thresholding greedy algorithm, in the case of general bases in Banach spaces. We show the …

We show that, for quasi-greedy bases in real or complex Banach spaces, an optimal bound
for the ratio between greedy N-term approximation∥ x− GN x∥ and the best N-term …

The last decade has seen great progress in the study of nonlinear approximation, which was
motivated by numerous applications. Nonlinear approximation is important in applications …

We study Lebesgue-type inequalities for greedy approximation with respect to quasi-greedy
bases. We mostly concentrate on this study in the Lp spaces. The novelty of the paper is in …

It is known that for a conditional quasi-greedy basis B in a Banach space X, the associated
sequence (km [B]) m= 1∞ of its conditionality constants verifies the estimate km [B]= O (log⁡ …

We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete
seminormalized biorthogonal systems in Banach spaces. The bounds are given only in …

For quasi-greedy bases 𝓑 in Hilbert spaces, we give—answering a question by Temlyakov—
an improved bound of the associated conditionality constants kN (𝓑)= O (logN) 1–ε, for some …

The purpose of this paper is to quantify the size of the Lebesgue constants associated with
the thresholding greedy algorithm in terms of a new generation of parameters that modulate …

We estimate the Lebesgue constants for the weak thresholding greedy algorithm in a
Banach space relative to a biorthogonal system. The estimates involve the weakness …