Every subsymmetric basis is greedy
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 have that any subsymmetric basis is 2-GUR. Let us now put our problem into context by summarizing its back-groung. Albiac and Wojtaszczyk exhibited in [4] an example of a 1- WebJul 1, 2024 · while a basis is greedy if and only if it is unconditional and democratic [22], a basis is almost greedy if and only if it is quasi-greedy and democratic (see ([ 14 ], Theo- …
Every subsymmetric basis is greedy
Did you know?
WebOct 20, 2015 · We say that ( e j) is greedy if there is C ≥ 1 such that for any x ∈ X and m ∈ N we have ‖ x − G m ( x) ‖ ≤ C inf ‖ x − y ‖, where the "inf" is taken over all y ∈ X which can be expressed as the linear combination of m elements of ( e j). A basis is symmetric when it is unconditional and equivalent to all its permutations. Weblems. We give examples of one-greedy bases that are not symmetric or subsymmetric, and examples of greedy bases that cannot be renormed so as to make them one …
WebDec 16, 2024 · Our aim in this article is to contribute to the study of the structure of subsymmetric basic sequences in Banach spaces (even, more generally, in quasi-Banach spaces). For that we introduce the... 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 type (other than the u.v.b. of c0 or ℓp). A second symmetric example was constructed in [7]. Recently, the first example of a
WebSep 1, 2011 · Here the authors found examples of non-subsymmetric greedy bases which are not 1-GUR (like the Haar basis in the dyadic Hardy space H 1 and the canonical … http://homepages.math.uic.edu/~rosendal/PapersWebsite/Haskell.pdf
WebKeywords: m-term approximation, greedy basis, renorming, symmetric basis, subsymmetric basis 2010 MSC: 41A65, 41A44, 41A50 Introduction In approximation …
WebNew characterizations of the unit vector basis of or chris mifsud bonniciWebIt 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 … chris mihailoffWebditionality constants, quasi-greedy basis, almost greedy basis, subsymmetric basis, superre exivity, sequence spaces, Banach spaces. F. Albiac and J.L. Ansorena are … chris mihailovichWebWe 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 ... chris mihailidis chelmsford maWebIt 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(logm) and that if the reverse inequality logm=O(k m [B]) holds then X is non-superreflexive. Indeed, it is known that a quasi-greedy basis in a superreflexive quasi … chris middleton nba wifeWebMar 25, 2016 · 1 Answer. In fact the definitin of subbasis is loose, take any finite intersection of elements from the subbasis to form open sets, along with the original set itself form a … chris mightonWebMotivated by Altshuler’s famous characterization of the unit vector basis of ... cratic, almost greedy, or invariant under spreading. However, we do not know the ... )is invariant under … geoffrey starr