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., nonHilbertian spaces that do not contain the direct sum of any two nonHilbertian 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.06286
 arXiv:
 arXiv:2012.06286
 Bibcode:
 2020arXiv201206286A
 Keywords:

 Mathematics  Functional Analysis;
 46B03;
 46B06;
 46B2546B28;
 46B45
 EPrint:
 49 pages,slight modifications in a couple of proofs, typos corrected