haracterization of (semi-)Eberlein compacta using retractional skeleton

Autor(es)

Correa, Claudia ^[1] ; Cuth, Marek ^{[2, 3]} ; Somaglia, Jacopo ^[4]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Ave Estados 5001, Santo Andre, SP - Brazil

^[2] Czech Acad Sci, Inst Math, Zitna 25, Prague 11567 1 - Czech Republic

^[3] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Prague 18675 8 - Czech Republic

^[4] Univ Milan, Dipartimento Matemat F Enriques, Via Cesare Saldini 50, I-20133 Milan - Italy

• Tipo de documento: Artigo Científico
• Fonte: STUDIA MATHEMATICA; v. 263, n. 2 NOV 2021.
• Citações Web of Science: 1

Resumo

We study retractions associated to suitable models in compact spaces admitting a retractional skeleton and find several interesting consequences. Most importantly, we provide a new characterization of Valdivia compacta using the notion of retractional skeletons, which seems to be helpful when characterizing their subclasses. Further, we characterize Eberlein and semi-Eberlein compacta in terms of retractional skeletons and show that our new characterizations give an alternative proof of the fact that a continuous image of an Eberlein compact is Eberlein as well as new stability results for the class of semi-Eberlein compacta, solving in particular an open problem posed by Kubis and Leiderman. (AU)

• Processo FAPESP: 19/08515-6 - Generalizações do teorema de Sobczyk para espaços de Banach da forma C(K)
• Beneficiário: Claudia Correa de Andrade Oliveira
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 18/09797-2 - Geometria dos Espaços de Banach da forma C(K)
• Beneficiário: Claudia Correa de Andrade Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Regular