Uncountable irredundant sets in nonseparable scattered C*-algebras (2019)
- Authors:
- Autor USP: HIDA, CLAYTON SUGUIO - IME
- Unidade: IME
- Sigla do Departamento: MAT
- Subjects: C* ÁLGEBRAS; TEORIA DOS CONJUNTOS; ESPAÇOS DE BANACH
- Keywords: Forcing; Irredundant sets; Scattered C*-algebras; Conjuntos irredundantes
- Agências de fomento:
- Language: Inglês
- Abstract: Given a C*-algebra $\A$, an irredundant set in $\A$ is a subset $\mathcal$ of $\A$ such that no $a\in \mathcal$ belongs to the C*-subalgebra generated by $\mathcal\setminus\{a\}$. Every separable C*-algebra has only countable irredundant sets and we ask if every nonseparable C*-algebra has an uncountable irredundant set. For commutative C*-algebras, if $K$ is the Kunen line then $C(K)$ is a consistent example of a nonseparable commutative C*-algebra without uncountable irredundant sets. On the other hand, a result due to S. Todorcevic establishes that it is consistent with ZFC that every nonseparable C*-algebra of the form $C(K)$, for a compact 0-dimensional space $K$, has an uncountable irredundant set. By the method of forcing, we construct a nonseparable and noncommutative scattered C*-algebra $\A$ without uncountable irredundant sets and with no nonseparable abelian subalgebras. On the other hand, we prove that it is consistent that every C*-subalgebra of $\B(\ell_2)$ of density continuum has an irredundant set of size continuum.
- Imprenta:
- Data da defesa: 05.07.2019
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ABNT
HIDA, Clayton Suguio. Uncountable irredundant sets in nonseparable scattered C*-algebras. 2019. Tese (Doutorado) – Universidade de São Paulo, São Paulo, 2019. Disponível em: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05082019-165942/. Acesso em: 11 jan. 2026. -
APA
Hida, C. S. (2019). Uncountable irredundant sets in nonseparable scattered C*-algebras (Tese (Doutorado). Universidade de São Paulo, São Paulo. Recuperado de http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05082019-165942/ -
NLM
Hida CS. Uncountable irredundant sets in nonseparable scattered C*-algebras [Internet]. 2019 ;[citado 2026 jan. 11 ] Available from: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05082019-165942/ -
Vancouver
Hida CS. Uncountable irredundant sets in nonseparable scattered C*-algebras [Internet]. 2019 ;[citado 2026 jan. 11 ] Available from: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05082019-165942/
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