相关论文: A note on partially-greedy bases in quasi-Banach s…
We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We…
In this paper, motivated by the notion of $w$-Property $(A)$ defined in [2], we introduce the notions of $w$-left Property $(A)$ and $w$-right Property $(A)$. We also introduce the notions of $w$-partially greedy basis (using a…
We prove thatthe Banach space $(\oplus_{n=1}^\infty \ell_p^n)_{\ell_q}$, which is isomorphic to certain Besov spaces, has a greedy basis whenever $1\leq p \leq\infty$ and $1<q<\infty$. Furthermore, the Banach spaces $(\oplus_{n=1}^\infty…
Greedy bases are those bases where the Thresholding Greedy Algorithm (introduced by S. V. Konyagin and V. N. Temlyakov) produces the best possible approximation up to a constant. In 2017, Bern\'a and Blasco gave a characterization of these…
We prove that the sequence spaces $\ell_p\oplus\ell_q$ and the spaces of infinite matrices $\ell_p(\ell_q)$, $\ell_q(\ell_p)$ and $(\bigoplus_{n=1}^\infty \ell_p^n)_{\ell_q}$, which are isomorphic to certain Besov spaces, have an almost…
We show that for quasi-greedy bases in real Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N-term error of approximation times a constant which depends on the democracy functions and the…
In this paper, we establish new advances in the theory started by T. Oikhberg in [15] where the author joins greedy approximation theory with the use of sequences with gaps. Concretely, we address and partially answer three open questions…
We show that for quasi-greedy bases in real or complex Banach spaces the error of the thresholding greedy algorithm of order N is bounded by the best N- term error of approximation times a function of N which depends on the democracy…
We characterize the approximation spaces of a broad class of bases - which includes almost greedy bases - in terms of weighted Lorentz spaces. For those bases, we also find necessary and sufficient conditions under which the approximation…
The general theory of greedy approximation with respect to arbitrary dictionaries is well developed in the case of real Banach spaces. Recently, some of results proved for the Weak Chebyshev Greedy Algorithm (WCGA) in the case of real…
The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to $c_0$, $\ell_2$, and all separable…
We generalize several theorems of R\'enyi, Parry, Dar\'oczy and K\'atai by characterizing the greedy and quasi-greedy expansions in non-integer bases.
We continue the study initiated in [F. Albiac and P. Wojtaszczyk, Characterization of $1$-greedy bases, J. Approx. Theory 138 (2006), no. 1, 65-86] of properties related to greedy bases in the case when the constants involved are sharp,…
We continue our study of the Thresholding Greedy Algorithm when we restrict the vectors involved in our approximations so that they either are supported on intervals of $\mathbb N$ or have constant coefficients. We introduce and…
In this paper we propose a unified way of analyzing a certain kind of greedy-type algorithms in Banach spaces. We define a class of the Weak Biorthogonal Greedy Algorithms that contains a wide range of greedy algorithms. In particular, we…
It is known that a basis is almost greedy if and only if the thresholding greedy algorithm gives essentially the smallest error term compared to errors from projections onto intervals or in other words, consecutive terms of $\mathbb{N}$. In…
We show that the Lindenstrauss basic sequence in l_1 may be used to construct a conditional quasi-greedy basis of l_1, thus answering a question of Wojtaszczyk. We further show that the sequence of coefficient functionals for this basis is…
In this paper we settle in the negative the problem of the superreflexivity of Garling sequence spaces by showing that they contain a complemented subspace isomorphic to a non superreflexive mixed-norm sequence space. As a by-product of our…
The goal of this paper is to study the performance of the Thresholding Greedy Algorithm (TGA) when we increase the size of greedy sums by a constant factor $\lambda\geqslant 1$. We introduce the so-called $\lambda$-almost greedy and…
In this paper, we study weights for the Thresholding Greedy Algorithm (TGA). While previous work focused on sequential weights $\varsigma = (s_n)_{n\in\mathbb{N}}$ on each positive integer, we study a more general weight $\omega =…