Fσ C-ideals as B-ideals

Determine whether every Fσ C-ideal is automatically a B-ideal.

Background

C-ideals arise from unconditional convergence, whereas B-ideals arise from weak unconditional convergence. The paper notes that the answer is affirmative for representations in c0, where an Fσ C-ideal must be summable, but leaves the general question unresolved.

References

This leads to the following question.Question 2.4. Is every Fσ C-ideal automatically a B-ideal?

— $F_σ$-ideals, colorings, and representation in Banach spaces  (2501.15643 - Lopez-Abad et al., 26 Jan 2025) in Question 2.4, Section 2, page 6

Question 2.4. Is every Fσ C-ideal automatically a B-ideal?

— $F_σ$-ideals, colorings, and representation in Banach spaces  (2501.15643 - Lopez-Abad et al., 26 Jan 2025) in Question 2.4, p. 6