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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 ...
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 ...
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 ...
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 ...
Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p ≤ 1
(Springer, 2021)
info:eu-repo/semantics/article,
Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for 0 < p ≤ 1 over the Euclidean spaces Rd and Zd. To that end, on one hand we show that Fp(Rd) admits a Schauder basis for every p ∈ 2 (0, ...
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 ...
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 ...