Let $\{Z(t)\}_{t\geq 0}$ be a semigroup of positive operators on a Banach lattice $X$. I want to show that
$$\int_0^1[Z(1-s)+Z(1+s)]fds-f\in X_+,\quad f\in X_+$$
Where $X_+$ denotes the positive part of $X$.
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Sign up to join this communityLet $\{Z(t)\}_{t\geq 0}$ be a semigroup of positive operators on a Banach lattice $X$. I want to show that
$$\int_0^1[Z(1-s)+Z(1+s)]fds-f\in X_+,\quad f\in X_+$$
Where $X_+$ denotes the positive part of $X$.