Invariant measures from locally bounded orbits

Motivated by recent investigations of Sophie Grivaux and Étienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X⟶X$ acting on a Fréchet space $X$, and we use this new notion to construct (non-trivial) $T$-invariant probability Borel measures on $(X,\mathcal{B}(X))$.