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Ultrapowers of Calderón-Lozanovskii interpolation spaces. (English) Zbl 0918.46065

Summary: We show that ultrapowers of Calderón interpolation spaces of a couple of Banach lattices with non-trivial concavity are obtained by Calderón interpolation from the ultrapowers of the given lattices. More generally ultrapowers of Calderón-Lozanovskii interpolation spaces are ‘generalized Calderón-Lozanovskii intermediate spaces’ between the ultrapowers. These results are extended to the situation of a couple of Köthe function spaces without concavity assumption.

MSC:

46M07 Ultraproducts in functional analysis
46M35 Abstract interpolation of topological vector spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B42 Banach lattices
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References:

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