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On the structure of ultraproducts of real interpolation spaces. (English) Zbl 1019.46017

In this paper, the authors investigate the relation between the ultraproducts of interpolation spaces (defined by the real interpolation method) between \(L^{p}\) spaces and the interpolation space on the canonical ultraproduct measure space. The latter is a complemented subspace of the former.

MSC:

46B70 Interpolation between normed linear spaces
46B08 Ultraproduct techniques in Banach space theory
46M35 Abstract interpolation of topological vector spaces
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