### Abstract

We introduce the notion of a weight-almost greedy basis and show that a basis for a real Banach space is w-almost greedy if and only if it is both quasi-greedy and w-democratic. We also introduce the notion of a weight-semi-greedy basis and show that a w-almost greedy basis is w-semi-greedy and that the converse holds if the Banach space has finite cotype.

Original language | English (US) |
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Pages (from-to) | 109-128 |

Number of pages | 20 |

Journal | Proceedings of the Steklov Institute of Mathematics |

Volume | 303 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1 2018 |

### ASJC Scopus subject areas

- Mathematics (miscellaneous)

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## Cite this

Dilworth, S. J., Kutzarova, D., Temlyakov, V., & Wallis, B. (2018). Weight-Almost Greedy Bases.

*Proceedings of the Steklov Institute of Mathematics*,*303*(1), 109-128. https://doi.org/10.1134/S0081543818080102