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Previous issue date: 2016-06-17 / Neste trabalho estudamos algumas extens˜oes do conceito de operadores multilineares
absolutamente somantes, generalizamos alguns resultados conhecidos e respondemos
parcialmente alguns problemas abertos. Para a classe das aplica¸c˜oes absolutamente
(p; q; r)-somantes, obtemos alguns resultados de coincidˆencia e inclus˜ao e mostramos
que o ideal de polinˆomios absolutamente (p; q; r)-somantes n˜ao ´e corente, de acordo
com a no¸c˜ao de ideais coerentes devida a D. Carando, V. Dimant e S. Muro. Para
contornar esta falha, introduzimos o conceito de aplica¸c˜oes m´ultiplo (p; q; r)-somantes
e mostramos que, com essa nova abordagem, o ideal de polinˆomios m´ultiplo (p; q; r)-
somantes ´e coerente e compat´ıvel com o ideal de operadores lineares absolutamente
(p; q; r)-somantes. / In this work we investigate some extensions of the concept of absolutely summing
operators, generalize some known results and provide partial answers to some open
questions. For the class of absolutely (p; q; r)-summing mappings we obtain some
inclusion and coincidence results and show that the ideal of absolutely (p; q; r)-summing
polynomials is not coherent, according to the notion of coherent ideals due to D.
Carando, V. Dimant and S. Muro. In order to bypass this deficiency, we introduce
the concept of multiple (p; q; r)-summing multilinear and polynomial operators and
show that, with this new approach, the ideal of multiple (p; q; r)-summing polynomials
is coherent and compatible with the ideal of absolutely (p; q; r)-summing operators.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufpe.br:123456789/17977 |
| Date | 17 June 2016 |
| Creators | BERNARDINO, Adriano Thiago Lopes |
| Contributors | http://buscatextual.cnpq.br/buscatextual/busca.do, PELLEGRINO, Daniel Marinho |
| Publisher | Universidade Federal de Pernambuco, Programa de Pos Graduacao em Matematica, UFPE, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Breton |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFPE, instname:Universidade Federal de Pernambuco, instacron:UFPE |
| Rights | Attribution-NonCommercial-NoDerivs 3.0 Brazil, http://creativecommons.org/licenses/by-nc-nd/3.0/br/, info:eu-repo/semantics/openAccess |
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