This is an announcement for the paper “Weight-almost greedy bases” by Stephen J. Dilworthhttps://arxiv.org/find/math/1/au:+Dilworth_S/0/1/0/all/0/1, Denka Kutzarovahttps://arxiv.org/find/math/1/au:+Kutzarova_D/0/1/0/all/0/1, Vladimir Temlyakovhttps://arxiv.org/find/math/1/au:+Temlyakov_V/0/1/0/all/0/1, Ben Wallishttps://arxiv.org/find/math/1/au:+Wallis_B/0/1/0/all/0/1.

Abstract: We introduce the notion of a \textit{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 \textit{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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1803.02932