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.