Work

Embedding $$\ell _2$$ and J into subspaces of JT and $$JT^*$$

Year: 2026

Type: article

Abstract: In the first part of the paper we show that every closed subspace of JT or $$JT^*$$ J T ∗ contains $$\ell _2$$ ℓ 2 complemented in JT or $$JT^*$$ J T ∗ respectively, and JT contains uncomplemented copies of $$\ell _2$$ ℓ 2 . As a result, the predual $$\mathcal {B}$$ B of JT , as well as the spaces JT and $$JT^*$$ J T ∗ , are subprojective and superprojective. In the second part, we prove that every weakly Cauchy sequence that is not weakly convergent in JT has a subsequence equivalent to the basis of J . Hence, every non-reflexive subspace of JT contains an isomorphic copy of J , and every Schauder basic sequence in JT has a subsequence which is equivalent either to the basis of $$\ell _2$$ ℓ 2 or to the basis of J . Moreover these subspaces may be selected to be complemented in JT .

Source: Revista Matemática Complutense

DOI: 10.1007/s13163-026-00588-2

Authors: Spiros A. Argyros, Manuel González, Pavlos Motakis

Institutions: National Technical University of Athens, Universidad de Cantabria, York University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Universidad de Cantabria