A property of interpolation spaces (Q5903866)

Let \(A_ i\) \((i=0,1,2)\) be Banach spaces continuously embedded in a Hausdorff topological vector space and let F be an interpolation functor. The author investigates cases when \(F(\{A_ 0,A_ 1\cap A_ 2\})=F(\{A_ 0,A_ 1\})\cap F(\{A_ 0,A_ 2\}\). He proves this to be true in the case when the \(A_ i\) are Banach lattices on (\(\Omega\),\(\mu)\) and F is any K-interpolation functor, or F is the Calderón functor \((F(A_ 0,A_ 1)=A_ 0^{1-\theta}A_ 1^{\theta})\).