 A Banach space is said to be "continuously embedded" in a Hausdorff topological vector space when is a linear subspace of such that the inclusion map from into is continuous.A compatible couple of Banach spaces consists of two Banach spaces and that are continuously embedded in the same Hausdorff topological vector space .The embedding in a linear space allows to consider the two linear subspaces

and

Interpolation does not depend only upon the isomorphic (nor isometric) equivalence classes of and .