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Addendum to "uniqueness of unconditional basis of infinite direct sums of quasi-Banach spaces"
(Springer, 2022)
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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 ...
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, ...
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 ...
Quasi-greedy bases in ℓp (0 < p < 1) are democratic
(Elsevier, 2020)
info:eu-repo/semantics/article,
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 c0, ℓ2, and all separable L1-spaces. ...
On a 'philosophical' question about Banach envelopes
(Springer, 2021)
info:eu-repo/semantics/article,
We show how to construct non-locally convex quasi-Banach spaces X whose dual separates the points of a dense subspace of X but does not separate the points of X. Our examples connect with a question raised by Pietsch (Rev ...
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 ...
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 ...