I've been reading probability formalisms, and I see people referring to expectation often as an operator, and less often as a functional (in the context of a vector space of random variables).
I can see how $\mathbb{E}: X \mapsto \mathbb{R}$ is a functional, in that it takes $X$, an element of a vector space over $\mathbb{R}$, and returns an element of that field. But I fail to see how it's an operator; in what sense is the expected value of a random variable itself a function? (Of course, there's the sense in which any constant function $X: \Omega \to \{r\}$ is a random variable, but that doesn't seem "clean" enough to motivate the separate treatment).