Multipliers for the Calderón construction

On the basis of a new approach to the Calderón construction $X_0^{\theta} X_1^{1-\theta}$ for ideal spaces $X_0$ and $X_1$ and a parameter $\theta \in [0,1]$, final results concerning a description of multipliers spaces are obtained. In particular, it is shown that if ideal spaces $X_0$ and $X_1$ have the Fatou property, then $M(X_0^{\theta_0} X_1^{1-\theta_0}\,{\to}\,X_0^{\theta_1} X_1^{1-\theta_1}) = M(X_1^{\theta_1 - \theta_0} \to X_0^{\theta_1 -\theta_0})$ for $0 <\theta_0 <\theta_1 <1$. Due to the absence of constraints on the ideal spaces $X_0$ and $X_1$, the obtained results apply to a large class of ideal spaces.