Variants of the James Tree space

S. A. Argyros; A. Manoussakis; P. Motakis

paper

Variants of the James Tree space

arXiv:2012.06286

Abstract

Recently, W. Cuellar Carrera, N. de Rancourt, and V. Ferenczi introduced the notion of $d_{2}$ -hereditarily indecomposable Banach spaces, i.e., non-Hilbertian spaces that do not contain the direct sum of any two non-Hilbertian subspaces. They posed the question of the existence of such spaces that are $ℓ_{2}$ -saturated. Motivated by this question, we define and study two variants $J T_{2, p}$ and $J T_{G}$ of the James Tree space $J T$ . They are meant to be classical analogues of a future space that will affirmatively answer the aforementioned question.

49 pages,slight modifications in a couple of proofs, typos corrected