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Counterexamples in isometric theory of symmetric and greedy bases
(Elsevier, 2024)
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We continue the study initiated in Albiac and Wojtaszczyk (2006) of properties related to greedy bases in the case when the constants involved are sharp, i.e., in the case when they are equal to 1. Our main goal here is ...
On the permutative equivalence of squares of unconditional bases
(Elsevier, 2022)
Artículo / Artikulua,
We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty-five year-old question raised by Casazza and Kalton ...
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 ...
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 ...
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 ...
Bidemocratic bases and their connections with other greedy-type bases
(Springer, 2023)
Artículo / Artikulua,
In nonlinear greedy approximation theory, bidemocratic bases have traditionally played the role of dualizing democratic, greedy, quasi-greedy, or almost greedy bases. In this article we shift the viewpoint and study them ...
Conditional quasi-greedy bases in non-superreflexive Banach spaces
(Springer, 2019)
info:eu-repo/semantics/article,
For a conditional quasi-greedy basis B in a Banach space, the associated conditionality constants km[B] verify the estimate km[B]=O(logm). Answering a question raised by Temlyakov, Yang, and Ye, several authors have studied ...
Greedy approximation for biorthogonal systems in quasi-Banach spaces
(Instytut Matematyczny, 2021)
info:eu-repo/semantics/article,
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems in quasi-Banach spaces from a functional-analytic point of view. If ...
Elton's near unconditionality of bases as a threshold-free form of greediness
(Elsevier, 2023)
Artículo / Artikulua,
Elton's near unconditionality and quasi-greediness for largest coefficients are two properties of bases that made their appearance in functional analysis from very different areas of research. One of our aims in this note ...
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 ...