A note about maximal almost-invariant subspaces and maximal hyperinvariant subspaces (Q2338605)

Let \(H\) be a separable infinite-dimensional Hilbert space and \(B(H)\) be the set of all bounded linear operators on. In the paper under review, the authors show that, if \(M\) is an almost-invariant subspace for \(T \in B(H)\), then every maximal almost-invariant subspace of \(M\) is of codimension \(1\) in \(M\). They describe the maximal hyperinvariant subspaces for normal operators with all the dimensions of eigenspaces at most \(1\) on \(H\). They show that, for each hyperinvariant subspace, all its maximal hyperinvariant subspaces are also of codimension \(1\) in it.