A non-stable semigroup for which the Lyapunov equation has a bounded invertible, positive solution.
The product of a densely defined, invertible operator with a bounded operator need not to be densely defined.
The sum of a contraction and a bounded contraction need not to be a contraction.
In this example we construct a bounded operator T for which T+B is never invertible for B's having norms suffiently small.
Back to my homepage