Stafney's lemma holds for several "classical" interpolation methods
Functional Analysis
2010-05-19 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0911.5719,
title = {Stafney's lemma holds for several "classical" interpolation methods},
author = {Alon Ivtsan},
journal= {arXiv preprint arXiv:0911.5719},
year = {2010}
}
Comments
13 pages. Some of the hypotheses of the main theorem are slightly weakened and thus the result can be extended to the more abstract interpolation method defined using the discrete generalised J-method.