Stafney's lemma holds for several "classical" interpolation methods
Abstract
Let (B0,B1) be a Banach pair. Stafney showed that one can replace the space F(B0,B1) with its subspace G(B0,B1) in the definition of the norm in the Calderon complex interpolation method on the strip if the element belongs to the intersection of the spaces Bi. We shall extend this result to a more general setting, which contains well-known interpolation methods: the Calderon complex interpolation method on the annulus, the Lions-Peetre real method (with several different choices of norms), and the Peetre "plus minus" method.
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