English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present new methods to obtain singular twisted sums $X\oplus_\Omega X$(i.e., exact sequences $0\to X\to X\oplus_\Omega X \to X\to 0$ in which thequotient map is strictly singular), in which $X$ is the interpolation spacearising from a complex interpolation scheme and $\Omega$ is the inducedcentralizer.  Although our methods are quite general, in our applications we are mainlyconcerned with the choice of $X$ as either a Hilbert space, or Ferenczi'suniformly convex Hereditarily Indecomposable space. In the first case, weconstruct new singular twisted Hilbert spaces, including the only known exampleso far: the Kalton-Peck space $Z_2$. In the second case we obtain the firstexample of an H.I. twisted sum of an H.I. space. We then use Rochberg'sdescription of iterated twisted sums to show that there is a sequence $\mathcalF_n$ 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 ofK\"othe function spaces and construct several examples involving reflexive$p$-convex K\"othe function spaces, which include the function version of theKalton-Peck space $Z_2$.

Singular twisted sums generated by complex interpolation