WebMar 15, 2024 · It is known that for a conditional quasi-greedy basis B in a Banach space X, the associated sequence ( k m [ B]) m = 1 ∞ of its conditionality constants verifies the estimate k m [ B] = O ( log m) and that if the reverse inequality log m = O ( k m [ B]) holds then X is non-superreflexive. Web2) Let (ei) be a subsymmetric basis and suppose that all subsymmetric block bases of (ei) are equivalent to (ei). Altshuler [4] constructed the first symmetric example of this …

BUILDING HIGHLY CONDITIONAL ALMOST GREEDY AND …

WebWe continue the study of 1-greedy bases initiated by Albiac and Wojtaszczyk (2006) [1]. We answer several open problems that they raised concerning symmetry properties of 1-greedy bases and the improving of the greedy constant by renorming. We show that ... how old is haystack rock

Renormings and symmetry properties of one-greedy bases

WebIt is known that for a conditional quasi-greedy basis B in a Banach space X, the associated sequence (k m [B]) m=1 ∞ of its conditionality constants verifies the estimate k m [B]=O(log⁡m) and that if the reverse inequality log⁡m=O(k m [B]) holds then X is non-superreflexive. Indeed, it is known that a quasi-greedy basis in a superreflexive quasi … Web10]) one immediately sees that 1-subsymmetric bases are always 2-greedy. Hence, since any subsymmetric basis becomes 1-subsymmetric under a suitable renorming, we … Websubsequence has a further subsequence equivalent to the basis. An application of Ramsey’s theorem would show that the basis is subsymmetric – but, obviously, not every subsymmetric basis is equivalent to the unit vector basis of c 0 or p (take the basis of Schlumprecht’s space S, for example; see [13]). Received 12 December 2002; revised ... how old is hazbin hotel