Quantifying shrinking and boundedly complete bases
Functional Analysis
2021-04-15 v1
Abstract
We investigate possible quantifications of R. C. James' classical work on bases and reflexivity of Banach spaces. By introducing new quantities measuring how far a basic sequence is from being shrinking and/or boundedly complete, we prove quantitative versions of James' famous characterisations of reflexivity in terms of bases. Furthermore, we establish quantitative versions of James' characterisations of reflexivity of Banach spaces with unconditional bases.
Keywords
Cite
@article{arxiv.2104.06497,
title = {Quantifying shrinking and boundedly complete bases},
author = {Dongyang Chen and Tomasz Kania and Yingbin Ruan},
journal= {arXiv preprint arXiv:2104.06497},
year = {2021}
}
Comments
16 pp