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

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

2009-11-30

arxiv.org/abs/0911.5719v2

Mathematics

Functional Analysis

13 pages. Some of the hypotheses of the main theorem are slightly weakened and thus the result can be extended to the more abs

Scientific paper

Let (B_0,B_1) be a Banach pair. Stafney showed that one can replace the space F(B_0,B_1) with its subspace G(B_0,B_1) 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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