AN ISOMETRICALLY UNIVERSAL BANACH SPACE INDUCED BY A NON-UNIVERSAL BOOLEAN ALGEBRA

Autor(es)

Brech, Christina ^[1] ; Koszmider, Piotr ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Caixa Postal 66281, BR-05314970 Sao Paulo - Brazil

^[2] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw - Poland

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 144, n. 5, p. 2029-2036, MAY 2016.
• Citações Web of Science: 1

Resumo

Given a Boolean algebra A, we construct another Boolean algebra B with no uncountable well-ordered chains such that the Banach space of real-valued continuous functions C(K-A) embeds isometrically into C(K-B), where K-A and K-B are the Stone spaces of A and B, respectively. As a consequence we obtain the following: If there exists an isometrically universal Banach space for the class of Banach spaces of a given uncountable density k, then there is another such space which is induced by a Boolean algebra which is not universal for Boolean algebras of cardinality k. Such a phenomenon cannot happen on the level of separable Banach spaces and countable Boolean algebras. This is related to the open question of whether the existence of an isometrically universal Banach space and of a universal Boolean algebra are equivalent on the nonseparable level (both are true on the separable level). (AU)

• Processo FAPESP: 12/24463-7 - Métodos combinatórios em Espaços de Banach
• Beneficiário: Christina Brech
• Modalidade de apoio: Auxílio à Pesquisa - Regular