5
votes
1answer
116 views

Is irreducibility sufficient for uniqueness of invariant distribution for a Feller Semigroup?

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.) ...
1
vote
0answers
214 views

weak mixing and spectral theorem

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 ...
1
vote
1answer
181 views

sum of Perron-Frobenius operators

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 ...