English

Uniqueness of unconditional bases in Banach spaces

Functional Analysis 2009-09-25 v1

Abstract

We prove a general result on complemented unconditional basic sequences in Banach lattices and apply it to give some new examples of spaces with unique unconditional basis. We show that Tsirelson space and certain Nakano spaces have the unique unconditional bases. We also construct an example of a space with a unique unconditional basis with a complemented subspace failing to have a unique unconditional basis.

Keywords

Cite

@article{arxiv.math/9610210,
  title  = {Uniqueness of unconditional bases in Banach spaces},
  author = {Peter G. Casazza and Nigel J. Kalton},
  journal= {arXiv preprint arXiv:math/9610210},
  year   = {2009}
}