On a generalization of Bourgain's tree index

Kevin Beanland; Ryan Causey

On a generalization of Bourgain's tree index

Functional Analysis 2016-03-04 v1

Authors: Kevin Beanland , Ryan Causey

Abstract

For a Banach space $X$ , a sequence of Banach spaces $(Y_n)$ , and a Banach space $Z$ with an unconditional basis, D. Alspach and B. Sari introduced a generalization of a Bourgain tree called a $(\oplus_n Y_n)_Z$ -tree in $X$ . These authors also prove that any separable Banach space admitting a $(\oplus_n Y_n)_Z$ -tree with order $\omega_1$ admits a subspace isomorphic to $(\oplus_n Y_n)_Z$ . In this paper we give two new proofs of this result.

Keywords

Banach space Bourgain tree tree index unconditional basis separable Banach space $(\oplus_n Y_n)_Z$-tree

Cite

@article{arxiv.1603.01133,
  title  = {On a generalization of Bourgain's tree index},
  author = {Kevin Beanland and Ryan Causey},
  journal= {arXiv preprint arXiv:1603.01133},
  year   = {2016}
}

On a generalization of Bourgain's tree index

Abstract

Keywords

Cite

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