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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On Ideals That Are Closed Under Continuous Endomorphisms

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Author(s):
Goncalves, Dimas Jose [1] ; Schuetzer, Waldeck [1] ; Talpo, Humberto Luiz [1]
Total Authors: 3
Affiliation:
[1] Univ Fed Sao Carlos, Dept Matemat, Rod Washington Luis, Km 235, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: COMMUNICATIONS IN ALGEBRA; v. 44, n. 6, p. 2583-2591, 2016.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support Opportunities: Research Projects - Thematic Grants