  A complex number $\lambda$ is called an extended eigenvalue of a bounded
linear operator $T$ on a Banach space $\B$ if there exists a non-zero bounded
linear operator $X$ acting on $\B$ such that $XT=\lambda TX$. We show that
there are compact quasinilpotent operators on a separable Hilbert space, for
which the set of extended eigenvalues is the one-point set ${1}$.
