Regularizability of superposition of inverse linear operators (Q1190049)

Let \(L_ 0(X,Y)\) be the linear continuous injective operators; \(X,Y\) are Banach spaces. If \(X\) is separable and \(A\in L_ 0(X,Y)\), then the regularizability of \(A^{-1}\) is equivalent to the subspace \(A^*Y^*\subset X^*\) being norming. This article investigates the problem of determining the triples \((X,Y,Z)\) of infinite-dimensional separable Banach spaces for which there exist operators \(A\in L_ 0(X,Y)\) and \(B\in L_ 0(Y,Z)\) such that \(A^{-1}\) and \(B^{-1}\) are regularizable but \((BA)^{-1}\) is not.