A question involving Markov processes

Question

Let $(S, \mathcal{B}, m)$ be a measurable space and $X_p := L^p(S, \mathcal{B}, m)$. Let $T_t \in \mathcal{L}(X_p, X_p)$ be a bounded linear operator defined by $$(T_t f)(x) = \int\limits_S P(t, x, dy) f(y), \;\; f \in X_p,$$ where $P(t, x, \cdot)$ is a transition probability.

What does it mean $T_t \cdot 1$? (I have to show that $T_t \cdot 1 = 1$).

Thank you!

Answer 1

Here, $1$ is the function $x \mapsto 1$ and $T_t \cdotp 1$ is $T_t1$.