Variants of the James Tree space

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 JT 2,p and JT G of the James Tree space JT . They are meant to be classical analogues of a future space that will affirmatively answer the aforementioned question.