Somebody can give me a hand with this?
Given the unitary operator $U=1+i\varepsilon F$ (where $\varepsilon$ is an infinitesimal escalar), in order to prove that $F$ is Hermitean:
$$UU^{+}=1$$
$$(1+i\varepsilon F) (1-i\varepsilon F^+)=1$$
$$1+i\varepsilon F-i\varepsilon F^+ +\varepsilon^2 FF^+=1$$
It seems that $F$ must be equal to $F^+$ to satisfy that expression, but how can the remaining term be equal to zero? $(\varepsilon^2 FF^+\overset{\large\text{?}} = 0)$
Canceling out the $1$ on both sides one obtains $i\varepsilon F-i\varepsilon F^+ +\varepsilon^2 FF^+=0$. Dividing by $\varepsilon$ one obtains $i F-iF^+ +\varepsilon FF^+=0$. Taking standard part one obtains $i F-iF^+=0$. Therefore $F=F^+$.