## Abstract

Let X be a real Banach space and let (f(n)) be a positive nondecreasing sequence. We consider systems of unit vectors (x_{i})^{∞}_{i }= _{1} in X which satisfy ∥∑_{i∈} _{A} ± x_{i}∥ ≥ A - f(A), for all finite A⊂ ∌ and for all choices of signs. We identify the spaces which contain such systems for bounded (f(n)) and for all unbounded (f(n)). For arbitrary unbounded (f(n)), we give examples of systems for which [x_{i}] is H.I., and we exhibit systems in all isomorphs of ℓ_{1} which are not equivalent to the unit vector basis of ℓ_{1}. We also prove that certain lacunary Haar systems in L_{1} are quasi-greedy basic sequences.

Original language | English (US) |
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Pages (from-to) | 214-241 |

Number of pages | 28 |

Journal | Journal of Approximation Theory |

Volume | 114 |

Issue number | 2 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Mathematics(all)
- Applied Mathematics

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