Exercise 3, § 3

(a) There exists a Banach space E, a continuous automorphism $u$ of E and a Riesz endomorphism $v$ of E such that $u\circ v$ is not a Riesz endomorphism. There even exist such that $u\circ v-v\circ u$ is of finite rank.

(b) There exists a Banach space E, an automorphism $u$ of E and an endomorphism of finite rank $h$ such that $u+h$ is not a Riesz endomorphism.