On the operators which are invertible modulo an operator ideal (Q2758186)

Let \(L(X,Y)\) be the set of all continuous linear operators from \(X\) into \(Y\), which are both assumed to be Banach spaces. The authors study the semigroups \({\mathcal A}_l\) and \({\mathcal A}_r\) of operators which are left and right invertible respectively, modulo an operator ideal \({\mathcal A}\) and investigate connections between \({\mathcal A}_l, {\mathcal A}_r\) and the radical \({\mathcal A}^{rad}\) of the ideal \({\mathcal A}\).