On the Semadeni derivative of Banach spaces C(K, X)
| dc.citation.issue | 266 | pt_BR |
| dc.citation.volume | 2 | pt_BR |
| dc.contributor.author | Candido, Leandro [UNIFESP] | |
| dc.contributor.authorLattes | http://lattes.cnpq.br/6975165037874387 | pt_BR |
| dc.coverage.spatial | Polônia | pt_BR |
| dc.date.accessioned | 2023-07-05T17:24:28Z | |
| dc.date.available | 2023-07-05T17:24:28Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | The Semadeni derivative of a Banach space X, denoted by S(X), is the quotient of the space of all weak* sequentially continuous functionals in X** by the canon- ical copy of X. In a remarkable 1960 paper, Z. Semadeni introduced this concept in order to prove that C([0, ω 1 ]) is not isomorphic to C([0, ω 1 ]) ⊕ C([0, ω 1 ]). Here we investigate this concept in the context of C(K, X) spaces. In our main result, we prove that if K is a Hausdorff compactum of countable height, then S(C(K, X)) is isometrically isomorphic to C(K, S(X)) for every Banach space X. Additionally, if X is a Banach space with the Mazur property, we explicitly find the derivative of C([0, ω 1 ] n , X) for each n ≥ 1. Further we obtain an example of a nontrivial Banach space linearly isomorphic to its derivative. | pt_BR |
| dc.description.sponsorship | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | pt_BR |
| dc.description.sponsorshipID | 2016/25574-8 | pt_BR |
| dc.format.extent | 225-240 | pt_BR |
| dc.identifier.doi | DOI: 10.4064/sm210810-9-12 | pt_BR |
| dc.identifier.uri | https://repositorio.unifesp.br/handle/11600/68458 | |
| dc.language | eng | pt_BR |
| dc.publisher | Adam Skalski | pt_BR |
| dc.relation.ispartof | Studia Mathematica | pt_BR |
| dc.rights | info:eu-repo/semantics/restrictedAccess | pt_BR |
| dc.subject | Banach spaces not isomorphic to their squares | pt_BR |
| dc.subject | isomorphisms of C(K, X) spaces | pt_BR |
| dc.subject | Mazur spaces | pt_BR |
| dc.title | On the Semadeni derivative of Banach spaces C(K, X) | pt_BR |
| dc.title.alternative | On the Semadeni derivative of Banach spaces C(K, X) | pt_BR |
| dc.type | info:eu-repo/semantics/article | pt_BR |
| unifesp.campus | Instituto de Ciência e Tecnologia (ICT) | pt_BR |
| unifesp.departamento | Ciência e Tecnologia | pt_BR |
| unifesp.graduacao | Não se aplica | pt_BR |
| unifesp.graduateProgram | Não se aplica | pt_BR |
| unifesp.knowledgeArea | Outra | pt_BR |