The correspondence $({\overline{L}},s)\mapsto\psi_{{\overline{L}},s}$ satisfies the following properties.

1. (1)

   Let ${\overline{L}}_{i}=(L_{i},\|\cdot\|_{i})$, $i=1,2$, be toric line bundles equipped with toric metrics and let $s_{i}$ be a toric section of $L_{i}$. Then

   $$\psi_{{\overline{L}}_{1}\otimes{\overline{L}}_{2},s_{1}\otimes s_{2}}=\psi_{{\overline{L}}_{1},s_{1}}+\psi_{{\overline{L}}_{2},s_{2}}.$$

2. (2)

   Let ${\overline{L}}=(L,\|\cdot\|)$ be a toric line bundle equipped with a toric metric and let $s$ be a toric section of $L$. Then

   $$\psi_{{\overline{L}}^{-1},s^{-1}}=-\psi_{{\overline{L}},s}.$$