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Lipschitz algebras and Lipschitz-Free spaces over unbounded metric spaces
(Oxford University Press, 2021)
Artículo / Artikulua,
We investigate a way to turn an arbitrary (usually, unbounded) metric space M into a bounded metric space B in such a way that the corresponding Lipschitz-free spaces F(M) and F(B) are isomorphic. The construction we provide ...
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 ...
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 ...
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 ℓ2⊕T(2)
(American Mathematical Society, 2022)
info:eu-repo/semantics/article,
We provide a new extension of Pitt’s theorem for compact operators between quasi-Banach lattices which permits to describe unconditional bases of finite direct sums of Banach spaces X1 · · · Xn as direct sums of unconditional ...
Projections and unconditional bases in direct sums of ℓp SPACES, 0<p≤∞
(Wiley, 2021)
info:eu-repo/semantics/article,
We show that every unconditional basis in a finite direct sum ⊕p∈Aℓp , with A ⊂ (0,∞], splits into unconditional bases of each summand. This settles a 40 years old question raised in 'A. Ortyński, Unconditional bases in ...
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 ...
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 ...
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 ...
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 ...