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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, ...
Building highly conditional almost greedy and quasi-greedy bases in Banach spaces
(Elsevier, 2019)
info:eu-repo/semantics/article,
It is known that for a conditional quasi-greedy basis B in a Banach space X, the associated sequence (k(m)[B](m=1)(infinity) of its conditionality constants verifies the estimate k(m)[B] = O(log m) and that if the reverse ...