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Previous issue date: 2017-02-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The goal of our work is to study the class of the Cohen strongly summing operators.
Initially, we present basic results from Functional Analysis that are necessary for the
development of the text and then we deal with sequence spaces which will be used to
de ne and study the classes of operators involved in this work, as necessarily the class
of the absolutely summing operators. We also study the sequence space of the Cohen-
Khalil strongly (q; p)-summable sequences and the sequence space of the Cohen strongly
p-summable sequences, as a particular instance of the former. From this, we de ne
the class of the Cohen strongly p-summing operators and the class of the Cohen-Khalil
strongly (s; r; p)-summing operators which, under certain conditions, are equivalent. We
conclude with a study, from the viewpoint of the operator ideal theory, using the abstract
environment created by G. Botelho and J. R. Campos, in order to show that p and Dp
are Banach ideals and the relations dual
p = Dp and Ddual
p = p are valid, where p and p
are conjugate indexes. / objetivo de nosso trabalho e estudar a classe dos operadores Cohen fortemente p-
somantes. Inicialmente, apresentamos resultados b asicos de An alise Funcional necess arios
ao desenvolvimento do texto e, em seguida, tratamos dos espa cos de sequ^encias que ser~ao
usados na de ni c~ao e estudo das classes de operadores envolvidas no trabalho, como necessariamente
a classe dos operadores absolutamente somantes. Apresentamos tamb em o
espa co das sequ^encias Cohen-Khalil fortemente (q; p)-som aveis e o espa co das sequ^encias
Cohen fortemente p-som aveis, como caso particular do primeiro. A partir disto, de -
nimos a classe dos operadores Cohen fortemente p-somantes e a classe dos operadores
Cohen-Khalil fortemente (s; r; p)-somantes que, sob certas condi c~oes, s~ao equivalentes.
Conclu mos com um estudo, sob o ponto de vista da teoria dos ideais de operadores,
usando o ambiente abstrato criado por G. Botelho e J. R. Campos, para mostrar que p
e Dp s~ao ideais de Banach e valem as rela c~oes dual
p = Dp e Ddual
p = p, onde p e p s~ao
ndices conjugados.
| Identifer | oai:union.ndltd.org:IBICT/oai:tede.biblioteca.ufpb.br:tede/9296 |
| Date | 21 February 2017 |
| Creators | Leite, Fábio da Silva de Siqueira |
| Contributors | Campos, Jamilson Ramos |
| Publisher | Universidade Federal da Paraíba, Programa de Pós-Graduação em Matemática, UFPB, Brasil, Matemática |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFPB, instname:Universidade Federal da Paraíba, instacron:UFPB |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 666657583566969084, 600, 600, 600, 600, -78633126427147401, -7090823417984401694, 2075167498588264571 |
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