Variants of the James tree space

期刊论文
发表日期：

2024年10月28日

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Spiros A. Argyros,
Antonis Manoussakis,
Pavlos Motakis

摘要

We introduce and study two variant JT_2,p and JT_G of James Tree space JT. Both spaces are non-Hilbertian, they contain subspaces isomorphic to ℓ₂, and all such subspaces are complemented. The space JT_2,p is reflexive with an unconditional basis and its non-Hilbertian subspaces contain ℓ_p. The space JT_G is non-reflexive and its non-Hilbertian subspaces contain c₀. These examples form the semiclassical basis for an exotic forthcoming construction related to a question of W. Cuellar Carrera, N. de Rancourt and V. Ferenczi.