Asymptotically isometric copies of l(1⨁0)
Yazarlar (1)
Prof. Dr. Veysel NEZİR Kafkas Üniversitesi, Türkiye
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Hacettepe Journal of Mathematics and Statistics (Q2) | ||
| Dergi ISSN | 2651-477X Dergi Bilgileri (2020) | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 06-2020 |
| Cilt / Sayı / Sayfa | 49 / 3 / 984–997 | DOI | 10.15672/hujms.507488 |
| Makale Linki | https://dergipark.org.tr/tr/doi/10.15672/hujms.507488 | ||
| UAK Araştırma Alanları |
Matematiksel Analiz
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| Özet |
| Using James’ Distortion Theorems, researchers have inquired relations between spacescontaining nice copies of c0 or ℓ 1 and the failure of the fixed point property for nonexpansivemappings especially after the fact that every classical nonreflexive Banach space containsan isometric copy of either ℓ 1 or c0. For instance, finding asymptotically isometric (ai) copies of ℓ 1 or c0 inside a Banach space reveals the space’s failure of the fixed point property for nonexpansive mappings. There has been many researches done using these tools developed by James and followed by Dowling, Lennard, and Turett mainly to see if a Banach space can be renormed to have the fixed point property for nonexpansive mappings when there is failure.In this paper, we introduce the concept of Banach spaces containing ai copies of ℓ 10 andgive alternative methods of detecting them. We show the relations between spaces containing these copies and the failure of the fixed point property for nonexpansive mappings.Finally, we give some remarks and examples pointing our vital result: if a Banach spacecontains an ai copy of ℓ 10, then it contains an ai copy of ℓ 1 but the converse does not hold. |
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