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• W3100105787 abstract "We show that Rochberg's generalizared interpolation spaces $mathscr Z^{(n)}$ arising from analytic families of Banach spaces form exact sequences $0to mathscr Z^{(n)} to mathscr Z^{(n+k)} to mathscr Z^{(k)} to 0$. 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 interpolation scale of $ell_p$ spaces, then $mathscr Z^{(2)}$ becomes the well-known Kalton-Peck $Z_2$ space; we then show that $mathscr Z^{(n)}$ is (or embeds in, or is a quotient of) a twisted Hilbert space only if $n=1,2$, which solves a problem posed by David Yost; and that it does not contain $ell_2$ complemented unless $n=1$. We construct another nontrivial twisted sum of $Z_2$ with itself that contains $ell_2$ complemented." @default.
• W3100105787 created "2020-11-23" @default.
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• W3100105787 date "2015-07-15" @default.
• W3100105787 modified "2023-09-27" @default.
• W3100105787 title "Complex interpolation and twisted twisted Hilbert spaces" @default.
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• W3100105787 doi "https://doi.org/10.2140/pjm.2015.276.287" @default.
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