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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/2CA78D75-DEDC-4F71-BFF0-35334682CD9D | ||
| Year | 2022 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| 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. https://doi.org/10.1017/fms.2022.101 | ||
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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.
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