Let $X_0, X_1$ be two real Banach spaces and let $X = (X_0, X_1)_{s, q}$ be the Banach space obtained by the K- or J-method of interpolation. Here, $0 < s < 1$, $1 < q < \infty$.
If one of $X_0$ or $X_1$ is uniformly convex (or both are), can we deduce that $X$ is uniformly convex as well ?
Using Google, I've found a result in the book "Espaces D'Interpolation Reels, Topologie Et Geometrie" from Bernard Beauzamy, but his definition of interpolation space differs from the K- or J-method.
Any reference is welcomed !