A property of interpolation spaces (Q5903723)

Let \(A_ 0\), \(A_ 1\) and \(A_ 2\), be Banach spaces continuously imbedded in some Hausdorff topological vector space, and let F be an interpolation functor. The author considers the question: \[ F(\{A_ 0,A_ 1\cap A_ 2\})=F(\{A_ 0,A_ 1\})\cap F(\{A_ 0,A_ 2\}). \]