A complex number $z$ is said to be 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 $XT=zTX$.

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 $\{1\}$. This answers negatively two questions raised by A.Lambert, S.Pertrovic and A.Biswas.