Product of operators - what is the standard notation

Question

Given $P_i$, $i=1,\ldots,n$ operators on a Hilbert space $H$. For $x \in H$, Does $\left( \prod_{i=1}^n P_i\right) (x)$ mean $$ \left(\prod_{i=1}^n P_i\right) (x) = P_1 \cdots P_n (x)$$ or $$ \left(\prod_{i=1}^n P_i\right) (x) = P_n \cdots P_1 (x)\text{ ?}$$

Answer 1

It's pretty ambiguous. I believe the standard would be:

$$ \left(\prod_i P_i\right)(x)=(P_1\cdots P_n)(x)=P_1(P_2(\cdots P_n(x)\cdots))$$

We'll see what the votes of my answer reveal.

I even recall seeing this notation mean $\left(\prod_i P_i\right)(x)=\prod_i(P_i(x))$ once before.