Characterization of 1-almost greedy bases

By Fernando Albiac, José L. Ansorena. 2015

50 citations recorded by the source corpus.

This article closes the cycle of characterizations of greedy-like bases in the “isometric” case initiated in Albiac and Wojtaszczyk (J. Approx. Theory 138(1):65–86, 2006) with the characterization of 1-greedy bases and continued in Albiac and Ansorena (J. Approx. Theory 201:7–12, 2016) with the characterization of 1-quasi-greedy bases. Here we settle the problem of providing a characterization of 1-almost greedy bases in Banach spaces. We show that a basis in a Banach space is almost greedy with almost greedy constant equal to 1 if and only if it has Property (A). This fact permits now to state that a basis is 1-greedy if and only if it is 1-almost greedy and 1-quasi-greedy. As a by-product of our work we also provide a tight estimate of the almost greedy constant of a basis in the non-isometric case.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6a20252fca60e6d295afa8a9354a3d8bf11d08e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Pablo M. Berná
2. Ó. Blasco
3. Gustavo Garrigós

In Mathematical Physics

1. Pablo M. Berná
2. Ó. Blasco
3. Gustavo Garrigós

Citations in the corpus

• Lebesgue inequalities for the greedy algorithm in general bases (2016, methodology): “akov [14] establishes that LN = O(1) if and only if B is unconditional and democratic. Explicit estimates for LN have been obtained in various contexts for greedy bases [25, 2, 5], quasi-greedy bases [23, 7, 9, 6, 1], and a few examples of non quasi-greedy bases [19, 20, 17]. The goal of this paper ”