The Kalton-Peck space as a spreading model
| Autor: | Suárez, Jesús |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Mathematica Scandinavica 2024 |
| Druh dokumentu: | Working Paper |
| Popis: | The so-called Kalton-Peck space $Z_2$ is a twisted Hilbert space induced, using complex interpolation, by $c_0$ or $\ell_p$ for any $1\leq p\neq 2<\infty$. Kalton and Peck developed a scheme of results for $Z_2$ showing that it is a very rigid space. For example, every normalized basic sequence in $Z_2$ contains a subsequence which is equivalent to either the Hilbert copy $\ell_2$ or the Orlicz space $\ell_M$. Recently, new examples of twisted Hilbert spaces, which are induced by asymptotic $\ell_p$-spaces, have appeared on the stage. Thus, our aim is to extend the Kalton-Peck theory of $Z_2$ to twisted Hilbert spaces $Z(X)$ induced by asymptotic $c_0$ or $\ell_p$-spaces $X$ for $1\leq p<\infty$. One of the novelties is to use spreading models to gain information on the isomorphic structure of the subspaces of a twisted Hilbert space. As a sample of our results, the only spreading models of $Z(X)$ are $\ell_2$ and $\ell_M$, whenever $X$ is as above and $p\neq 2$. Comment: 35 pages |
| Databáze: | arXiv |
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