Made available in DSpace on 2015-05-15T11:46:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 519154 bytes, checksum: e1f2c33c19a740684327d51d9d1278f5 (MD5) Previous issue date: 2010-01-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we investigate recent results involving lineability and spaceability and the nonlinear theory of absolutely summing mappings. / Neste trabalho estudamos resultados recentes envolvendo o conceito de lineabilidade e espaçabilidade e a teoria não-linear de aplicações absolutamente somantes.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-10-11T18:36:34Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese Adriano Thiago.pdf: 1085326 bytes, checksum: 498b2bcfd47961466edce3360e11a858 (MD5) / Made available in DSpace on 2016-10-11T18:36:34Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese Adriano Thiago.pdf: 1085326 bytes, checksum: 498b2bcfd47961466edce3360e11a858 (MD5) 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.