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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 ...
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 ...
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 ...
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 ...
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 ...