If we have a couple of two compatible banach spaces (in this sense) $(X,Y)$ and a sequence of Banach spaces $\{Z\}_{\theta\in[0,1]}$ which are intermediate between $X$ and $Y$ satisfying:
- $Z_0=X$, $Z_1=Y$
- $\|f\|_{Z_\theta}\leq\|f\|_{X}^{1-\theta}\|f\|_{{Y}}^{\theta}$ for every $\theta\in[0,1]$.
Can we deduce under these conditions that $(X,Y)_{\theta}=Z_{\theta}$? Where $(X,Y)_{\theta}$ is the complex interpolation space between $X$ and $Y$.
