Let $(T_t)$ be a strongly continuous semigroup of positive operators on $C(K)$, where $K$ is a compact space. Assume also that $T_t1 =1 $ for every $t\geq 0$. (This is also called a Feller Semigroup.) ...
I'm trying to prove an equivalent statement about weak mixing transformations that relies on the spectral theorem, but I can't find a reference to fill in the last details. A hint for solving it or ...
My operator is the transfer operator $P$ on $L^1$ functions defined on compact $X$. It is the pre-dual of the operator $U:L^∞ \rightarrow L^∞$ defined by $U(ϕ)=ϕ\circ f$, for a fixed map f on X. I ...