Variants of the James Tree space

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

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arXiv · 2012.06286

Variants of the James Tree space

S. A. Argyros·A. Manoussakis·P. Motakis

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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 $\ell_2$-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.

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BibTeX RIS

S. A. Argyros, A. Manoussakis, P. Motakis. 2020-12-11. Variants of the James Tree space. https://arxiv.org/abs/2012.06286

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