Variants of the James Tree space
S.A.Argyros, A. Manoussakis, P. Motakis

TL;DR
This paper introduces variants of the James Tree space to explore the existence of $ ext{ell}_2$-saturated, hereditarily indecomposable Banach spaces, addressing a question about their structure and properties.
Contribution
The paper defines and studies two new variants of the James Tree space, providing a framework for future spaces that could be $ ext{ell}_2$-saturated and hereditarily indecomposable.
Findings
Defined two variants of the James Tree space, $JT_{2,p}$ and $JT_G$.
Provided structural analysis of these variants.
Laid groundwork for constructing $ ext{ell}_2$-saturated hereditarily indecomposable spaces.
Abstract
Recently, W. Cuellar Carrera, N. de Rancourt, and V. Ferenczi introduced the notion of -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 -saturated. Motivated by this question, we define and study two variants and of the James Tree space . They are meant to be classical analogues of a future space that will affirmatively answer the aforementioned question.
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Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory · Holomorphic and Operator Theory
