A note on bounded, conservative, linear operators and the maximal group (Q1196374)

Let \(Y\) be a complete subspace of a Banach space \(X\). Denote the collection of operators in \(X\) which leave \(Y\) invariant by \({\mathcal T}\). Write \({\mathcal M}\) for the maximal group of invertible elements in \({\mathcal T}\), \({\mathcal B}\) for the boundary of \({\mathcal M}\), and \({\mathcal N}\) for the complement of the closure of \({\mathcal M}\) in \({\mathcal N}\). The author examines the locations of products of pairs of operators taken from these three classes.