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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, ...
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. ...
Embeddability of ℓp and bases in Lipschitz free p-spaces for 0 < p ≤ 1
(Elsevier, 2020)
info:eu-repo/semantics/article,
Our goal in this paper is to continue the study initiated by the authors in of the geometry of the Lipschitz free p-spaces over quasimetric spaces for 0 < p ≤ 1, denoted Fp(M). Here we develop new techniques to show that, ...