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arXiv 2012.062862020-12math.FA

Variants of the James Tree space

S. A. Argyros, A. Manoussakis, P. Motakis

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

英文摘要：

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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