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- W2270015785 abstract "We present new methods to obtain singular twisted sums $Xoplus_Omega X$ (i.e., exact sequences $0to Xto Xoplus_Omega X to Xto 0$ in which the quotient map is strictly singular), in which $X$ is the interpolation space arising from a complex interpolation scheme and $Omega$ is the induced centralizer. Although our methods are quite general, in our applications we are mainly concerned with the choice of $X$ as either a Hilbert space, or Ferenczi's uniformly convex Hereditarily Indecomposable space. In the first case, we construct new singular twisted Hilbert spaces, including the only known example so far: the Kalton-Peck space $Z_2$. In the second case we obtain the first example of an H.I. twisted sum of an H.I. space. We then use Rochberg's description of iterated twisted sums to show that there is a sequence $mathcal F_n$ of H.I. spaces so that $mathcal F_{m+n}$ is a singular twisted sum of $mathcal F_m$ and $mathcal F_n$, while for $l>n$ the direct sum $mathcal F_n oplus mathcal F_{l+m}$ is a nontrivial twisted sum of $mathcal F_l$ and $mathcal F_{m+n}$. We also introduce and study the notion of disjoint singular twisted sum of Kothe function spaces and construct several examples involving reflexive $p$-convex Kothe function spaces, which include the function version of the Kalton-Peck space $Z_2$." @default.
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- W2270015785 date "2014-10-20" @default.
- W2270015785 modified "2023-10-01" @default.
- W2270015785 title "Singular twisted sums generated by complex interpolation" @default.
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