7. If the inequality
$$
2 \sin ^{2} C+\sin A \cdot \sin B>k \sin B \cdot \sin C
$$

holds for any $\triangle A B C$, then the maximum value of the real number $k$ is . $\qquad$
7. $2 \sqrt{2}-1$

From the problem, we know
$$
\begin{array}{l}
k\frac{2 c}{b}+\frac{b-c}{c}=\frac{2 c}{b}+\frac{b}{c}-1 \\
\geqslant 2 \sqrt{2}-1,
\end{array}
$$

Therefore, the maximum value of $k$ is $2 \sqrt{2}-1$.