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Complex interpolation and twisted twisted Hilbert spaces

2015
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Pacific Journal of Mathematics
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We show that Rochberg's generalizared interpolation spaces Z^(n) arising from analytic families of Banach spaces form exact sequences 0→ Z^(n)→ Z^(n+k)→ Z^(k)→ 0. We study some structural properties of those sequences; in particular, we show that nontriviality, having strictly singular quotient map, or having strictly cosingular embedding depend only on the basic case n=k=1. If we focus on the case of Hilbert spaces obtained from the interpolation scale of ℓ_p spaces, then Z^(2) becomes the

doi:10.2140/pjm.2015.276.287
fatcat:zbiyfom7nfdgvguxqsgqy4tqaq