On Ideals That Are Closed Under Continuous Endomorphisms

Autor(es)

Goncalves, Dimas Jose ^[1] ; Schuetzer, Waldeck ^[1] ; Talpo, Humberto Luiz ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, Rod Washington Luis, Km 235, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN ALGEBRA; v. 44, n. 6, p. 2583-2591, 2016.
• Citações Web of Science: 0

Resumo

Let F be the field R or C, and let F < X > be the free associative algebra generated by the infinite set X. If f F < X >, define its norm f as the sum of the absolute value of its coefficients. We describe the ideals of F < X > which are closed under all continuous endomorphisms of F < X >. An element f in the completion (F < X >) over bar is called a series identity for a normed algebra A if f belongs to the intersection of the kernels of all continuous homomorphisms from <(F < X >)over bar to A. We describe such identities for a nil Banach algebra. (AU)

• Processo FAPESP: 14/09310-5 - Estruturas algébricas e suas representações
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Temático