Derivation of vector-valued complex interpolation scales

Castillo, Jesús M. F.; Morales, Daniel A.; Fuente, Jesús Suárez de la

doi:10.1016/j.jmaa.2018.08.028

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Cited by 5 publications

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“…Indeed, for a long time, the only known examples were the Enflo-Lindenstrauss-Pisier space ( [10]) that we denote ℓ 2 (E n ), and the Kalton-Peck space Z 2 ([18]). This paper provides a few more examples, somehow continuing the work in [8,27] and [28].…”

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confidence: 86%

Some more twisted Hilbert spaces

Morales

Fuente

2021

Ann. Fenn. Math.

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We provide three new examples of twisted Hilbert spaces by considering properties that are "close" to Hilbert. We denote them Z(J ), Z(S 2 ) and Z(T 2 s ). The first space is asymptotically Hilbertian but not weak Hilbert. On the opposite side, Z(S 2 ) and Z(T 2 s ) are not asymptotically Hilbertian. Moreover, the space Z(T 2 s ) is a HAPpy space and the technique to prove it gives a "twisted" version of a theorem of Johnson and Szankowski (Ann. of Math. 176:1987-2001, 2012. This is, we can construct a nontrivial twisted Hilbert space such that the isomorphism constant from its n-dimensional subspaces to ℓ n 2 grows to infinity as slowly as we wish when n → ∞.

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