Properties of B-ideals generated by 1-subsymmetric bases

Investigate the properties of B((x_k)_k) when (x_k)_k is a 1-subsymmetric basis.

Background

A 1-subsymmetric basis is invariant under passage to subsequences in the sense that finite linear combinations have the same norm on every increasing choice of indices. The paper explicitly asks for a systematic study of the B-ideals generated by such bases.

References

Question 2.6. Study the properties of B((x_k)_k) when (x_k)_k is a 1-subsymmetric basis.

— $F_σ$-ideals, colorings, and representation in Banach spaces  (2501.15643 - Lopez-Abad et al., 26 Jan 2025) in Question 2.6, p. 7