Stafney's lemma holds for several "classical" interpolation methods

2009/11/30 by Ivtsan, Alon
#46B45 (secondary) #46B70 (primary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0911.5719

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 B_i. 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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