The singularly continuous spectrum and non-closed invariant subspaces

Vadim Kostrykin, Konstantin A. Makarov

Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and ${\mathfrak{H}}_0\subset \mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$.…