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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 $\mathscr Z^{(n)}$ arising from analytic families of Banach spaces form exact sequences $0\to \mathscr Z^{(n)} \to \mathscr Z^{(n+k)} \to \mathscr Z^{(k)} \to 0$. 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

doi:10.2140/pjm.2015.276.287
fatcat:zbiyfom7nfdgvguxqsgqy4tqaq