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Weak forms of unconditionality of bases in greedy approximation
(Instytut Matematyczny, 2022)
Artículo / Artikulua,
We study a new class of bases, weaker than quasi-greedy bases, which retain their unconditionality properties and can provide the same optimality for the thresholding greedy algorithm. We measure how far these bases are ...
Addendum to "uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces"
(Springer, 2022)
Artículo / Artikulua,
After [Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces, Positivity 26 (2022), Paper no. 35] was published, we realized that Theorem 4.2 therein, when combined with work of Casazza and Kalton ...
Uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces
(Kluwer Academic Publishers, 2022)
Artículo / Artikulua,
This paper is devoted to providing a unifying approach to the study of the uniqueness of unconditional bases, up to equivalence and permutation, of infinite direct sums of quasi-Banach spaces. Our new approach to this type ...
On certain subspaces of p for 0 < p ≤ 1 and their applications to conditional quasi-greedy bases in p-Banach spaces
(Springer, 2021)
info:eu-repo/semantics/article,
We construct for each 0<p≤1 an infinite collection of subspaces of ℓp that extend the example of Lindenstrauss (Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12, 539–542, 1964) of a subspace of ℓ1 with no ...
Lipschitz free p-spaces for 0 < p < 1
(SpringerHebrew University Magnes Press, 2020)
info:eu-repo/semantics/article,
This paper initiates the study of the structure of a new class of p-Banach spaces, 0 <p < 1, namely the Lipschitz free p-spaces (alternatively called Arens—Eells p-spaces) Fp(M) over p-metric spaces. We systematically ...
Non-superreflexivity of Garling sequence spaces and applications to the existence of special types of conditional bases
(Instytut Matematyczny, 2020)
info:eu-repo/semantics/article,
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, ...
Sparse approximation using new greedy-like bases in superreflexive spaces
(Instytut Matematyczny, 2023)
Artículo / Artikulua,
This paper is devoted to theoretical aspects of optimality of sparse approximation. We undertake a quantitative study of new types of greedy-like bases that have recently arisen in the context of non-linear m-term approximation ...
Uniqueness of unconditional basis of Hp(T) ⊕ 2 and Hp(T) ⊕ T (2) for 0 < p < 1
(Elsevier, 2022)
Artículo / Artikulua,
Our goal in this paper is to advance the state of the art of
the topic of uniqueness of unconditional basis. To that end
we establish general conditions on a pair (X, Y) formed by a
quasi-Banach space X and a Banach ...
New parameters and Lebesgue-type estimates in greedy approximation
(Cambridge University Press, 2022)
Artículo / Artikulua,
The purpose of this paper is to quantify the size of the Lebesgue constants (𝑳𝑚)∞
𝑚=1 associated with the thresholding
greedy algorithm in terms of a new generation of parameters that modulate accurately some features ...
Lipschitz free spaces isomorphic to their infinite sums and geometric applications
(American Mathematical Society, 2021)
info:eu-repo/semantics/article,
We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct _1-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free ...