Stafney’s lemma holds for several “classical” interpolation methods

Ivtsan, Alon

doi:10.1090/S0002-9939-2011-10974-2

Stafney’s lemma holds for several “classical” interpolation methods
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by Alon Ivtsan PDF

Proc. Amer. Math. Soc. 140 (2012), 881-889 Request permission

Abstract:

Let $\left (B_{0},B_{1}\right )$ be a Banach pair. Stafney showed that one can replace the space $\mathcal {F}\left (B_{0},B_{1}\right )$ by its dense subspace $\mathcal {G}\left (B_{0},B_{1}\right )$ in the definition of the norm in the Calderón complex interpolation method on the strip if the element belongs to the intersection of the spaces $B_{i}$. We shall extend this result to a more general setting, which contains well-known interpolation methods: the Calderón complex interpolation method on the annulus, the Lions-Peetre real method (with different choices of norms), and the Peetre “$\pm$” method.

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