Show that there are linear operators T on the Hilbert space H what are not orthogonal projections, but their spectrum consists of the eigenvalues $\{0,1\}.$
I can not come up with an counterexample, but I suppose it must be infinite dimension? Hilbert spaces has orthogonal bases and I did an exersice showing that for projections $T'(T-I) = 0$ So obviously $T \neq TT'$, is zero some kind of accumulation point?