Subideals of operators. II (Q1946575)

The authors continue the work begun in Part~I of this series [J. Oper. Theory 70, No. 2, 355--373 (2013; \url{doi:10.7900/jot.2011sep02.1926})], investigating \(J\)-ideals on \(B(H)\) of the type \((\mathcal{S})_J\), which are generated by arbitrary sets \(\mathcal{S} \subset J\) of varying cardinality. The main results presented establish, for \(|\mathcal{S}| < \mathfrak{c}\), necessary and sufficient conditions for \((\mathcal{S})_J\) to be a \(B(H)\)-ideal and an algebraic structure for the \(J\)-ideal \((\mathcal{S})_J\). In the last section of this interesting paper, the authors discuss some questions posed in Part I from the perspective of the new results, and pose some questions about \(J\)-ideals.