7. If the quadratic function $f(x)=a x^{2}-2 x-a$ satisfies
$$
f(2)<f(1)<f(3)<f(0) \text {, }
$$

then the range of the real number $a$ is $\qquad$.
7. $\left(\frac{1}{2}, \frac{2}{3}\right)$.

From $f(2)<f(1)<f(3)$, we know that the quadratic function opens upwards, and the axis of symmetry is between $[1,2]$.

From $f(2)<f(1)$, we know that the axis of symmetry is in $\left(\frac{3}{2}, 2\right)$, i.e., the x-coordinate of the vertex $\frac{1}{a} \in\left(\frac{3}{2}, 2\right)$, which gives $a \in\left(\frac{1}{2}, \frac{2}{3}\right)$.