# $U(\Lambda)$ that implements Lorentz transformations on the states of Hilbert space is unitary

In Peskin & Schroeder QFT book p.59, they said:

The operator $$U(\Lambda)$$ that implements Lorentz transformations on the states of Hilbert space is unitary, even thought for boosts $$\Lambda_{1/2}$$ is not unitary.

Why the former $$U(\Lambda)$$ on the states of Hilbert space is unitary?

Why the not unitary $$\Lambda_{1/2}$$ would not affect the $$U(\Lambda)$$ on the states of Hilbert space being unitary or not?