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Institutional Repository [SANDBOX]
Technical University of Crete
Technical University of Crete
EN
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| URI | http://purl.tuc.gr/dl/dias/2CA78D75-DEDC-4F71-BFF0-35334682CD9D | - |
| Identifier | https://doi.org/10.1017/fms.2022.101 | - |
| Identifier | https://www.cambridge.org/core/product/F6603CD6B017AF811274B8C5EBE1323B | - |
| Language | en | - |
| Extent | 47 pages | en |
| Title | The complete separation of the two finer asymptotic ℓp structures for 1≤p<∞ | en |
| Creator | Argyros, Spiros, 1950- | en |
| Creator | Georgiou Alexandros | en |
| Creator | Manousakis Antonios | en |
| Creator | Μανουσακης Αντωνιος | el |
| Creator | Motakis, Pavlos | en |
| Publisher | Cambridge University Press | en |
| Content Summary | For 1 ≤ 𝑝 < ∞, we present a reflexive Banach space 𝔛( 𝑝)awi , with an unconditional basis, that admits ℓ𝑝 as a unique asymptotic model and does not contain any Asymptotic ℓ𝑝 subspaces. Freeman et al., Trans. AMS. 370 (2018), 6933–6953 have shown that whenever a Banach space not containing ℓ1, in particular a reflexive Banach space, admits 𝑐0 as a unique asymptotic model, then it is Asymptotic 𝑐0. These results provide a complete answer to a problem posed by Halbeisen and Odell [Isr. J. Math. 139 (2004), 253–291] and also complete a line of inquiry of the relation between specific asymptotic structures in Banach spaces, initiated in a previous paper by the first and fourth authors. For the definition of 𝔛 ( 𝑝)awi , we use saturation with asymptotically weakly incomparable constraints, a new method for defining a norm that remains small on a well-founded tree of vectors which penetrates any infinite dimensional closed subspace. | en |
| Type of Item | Peer-Reviewed Journal Publication | en |
| Type of Item | Δημοσίευση σε Περιοδικό με Κριτές | el |
| License | http://creativecommons.org/licenses/by/4.0/ | en |
| Date of Item | 2024-02-23 | - |
| Date of Publication | 2022 | - |
| Subject | Asymptotic structures | en |
| Bibliographic Citation | S. A. Argyros, A. Georgiou, A. Manoussakis, and P. Motakis, “The complete separation of the two finer asymptotic ℓp structures for 1≤p<∞,” Forum Math. Sigma, vol. 10, Dec. 2022, doi:10.1017/fms.2022.101. | en |
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