We begin by proving Furstenberg's Theorem, which tells us that if $f \colon X \to X$ is a weakly mixing system then any $n$-fold product

$$f \times \cdots \times f \colon X \times \cdots \times X \to X \times \cdots \times X$$

is automatically transitive.

Afterwards we introduce linear dynamical systems on Banach spaces, and construct an example of a linear dynamical system that is weakly mixing but not mixing.

Here are today's notes: