My question is concerned a point in this 1968 paper by Ion Suciu which is given in Theorem 2. In the last paragraph of page 104, it is claimed that $N$ (given in the formula 2.5) is a wandering subspace. I do not get this point.
(Reference: I. Suciu, On the semi-groups of isometries. Studia Math. 30 1968 101-110.)