In Weinberg's QFT textbook (volume 1), he proved the symmetry representation theorem in Appendix A, chapter 2, which states
Any symmetry transformation can be represented on the Hilbert space of physical states by an operator that is linear and unitary or antilinear and antiunitary.
But in section 5.4 (on page 218), he showed that the representation of the homogeneous Lorentz group is not unitary.
Do these two statements contradict with each other? Is the catch here the fact that the representation of the Lorentz group don't really act on Hilbert space?