The relationship between almost Dunford-Pettis operators and almost limited operators

Fahri, Kamal El; H’michane, Jawad

doi:10.2989/16073606.2015.1096854

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…A similar result for the second adjoint T * * is also proved. The results of these sections extend and generalize the known results on the topic, especially those from [3,9,11]. Finally, in Section 5 we prove when the second adjoint of an order weakly compact operator is almost Dunford-Pettis.…”

Section: Introductionsupporting

confidence: 73%

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Adjoints and second adjoints of almost Dunford-Pettis operators

Botelho¹,

Garcı́a²

2022

Preprint

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We investigate when the adjoint T * and the second adjoint T * * of an operator T betweeen Banach lattices is almost Dunford-Pettis. First we show when T * * is almost Dunford-Pettis for every T . Then we prove when T * or T * * is almost Dunford-Pettis whenever T is positive and almost Dunford-Pettis. Finally we prove when T * * is an almost Dunford-Pettis operator whenever T is order weakly compact.

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Section: Introductionsupporting

confidence: 73%

“…In this paper investigate when the adjoint and the second adjoint of an operator are almost Dunford-Pettis. These and related problems were treated in, e.g., [3,9,11].…”

Section: Introductionmentioning

confidence: 99%

Adjoints and second adjoints of almost Dunford-Pettis operators

Botelho¹,

Garcı́a²

2022

Preprint

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“…In [6] it is also constructed numerous distinguished examples of Banach spaces with or without the DP p property. Since the Dunford-Pettis property of order p for Banach spaces and especially Banach lattices was intensively studied by many authors, see for example [1,10,19,20,31]. A more general notion than the DP p property was proposed by Karn and Sinha [26].…”

Section: Definition 12 ([23]mentioning

confidence: 99%

Dunford–Pettis type properties and the Grothendieck property for function spaces

Gabriyelyan

Ka̧kol

2019

Rev Mat Complut

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For a Tychonoff space X, let C k (X) and Cp(X) be the spaces of real-valued continuous functions C(X) on X endowed with the compact-open topology and the pointwise topology, respectively. If X is compact, the classic result of A. Grothendieck states that C k (X) has the Dunford-Pettis property and the sequential Dunford-Pettis property. We extend Grothendieck's result by showing that C k (X) has both the Dunford-Pettis property and the sequential Dunford-Pettis property if X satisfies one of the following conditions: (i) X is a hemicompact space, (ii) X is a cosmic space (=a continuous image of a separable metrizable space), (iii) X is the ordinal space [0, κ) for some ordinal κ, or (vi) X is a locally compact paracompact space. We show that if X is a cosmic space, then C k (X) has the Grothendieck property if and only if every functionally bounded subset of X is finite. We prove that Cp(X) has the Dunford-Pettis property and the sequential Dunford-Pettis property for every Tychonoff space X, and Cp(X) has the Grothendieck property if and only if every functionally bounded subset of X is finite.2000 Mathematics Subject Classification. Primary 46A03; Secondary 54H11. Key words and phrases. function space, Dunford-Pettis property, Grothendieck property. Jerzy Kakol gratefully acknowledges the nancial support he received from the Center for Advanced Studies in Mathematics of the Ben Gurion University of the Negev during his visit April, 2018.

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“…Nossos resultados são sobre biadjuntos e extensões de Arens (ou de Aron-Berner) de operadores lineares e multilineares entre espaços de Riesz e reticulados de Banach. Resultados neste ambiente foram obtidos em, por exemplo, [6,7,22,26,29,43,44,80].…”

Section: Introductionunclassified

Extensões biduais de operadores lineares e multilineares entre espaços de Riesz e reticulados de Banach

Santisteban¹

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A maior recompensa para o trabalho do homem não é o que ele ganha com isso, mas o que ele se torna com isso.-Jhon Ruskin Agradeço a Deus por estar com boa saúde e pela força que me dá dia a dia para seguir em frente com meus objetivos traçados.Aos meus pais, Paula Santisteban Llauce e Luciano Garcia Chapoñan, a minhas irmãs Felicita, Carmen, Laura, Nelly e Delcy, a meus irmãos Genaro e Lorenzo e a todos meus sobrinhos e minhas sobrinhas. Todos eles são parte de minha vida e são meu motivo para seguir em frente e lograr meus objetivos.A Kassandra, pelo companhia e apoio durante meu Doutorado.Ao meu orientador, Geraldo Botelho, por ter aceitado ser meu orientador no meu Doutorado, pelo apoio e paciência durante o desenvolvimento desta tese.Pelo carinho e pela ajuda na estadia em Uberlândia, agradeço a Sirlene Cardoso, minha mãe Brasileira e a Sonia, uma das melhores amigas que conheci em São Paulo. Estou muito grato a vocês.A CAPES, pelo apoio financeiro durante os quatro anos de Doutorado.Ao programa de Doutorado em Matemática do Instituto de Matemática e Estatística. É uma honra para mim, ter a oportunidade de realizar meus estudos de doutorado com as condições necessárias durante estes quatro anos de formação e pesquisa. ResumoLuis Alberto Garcia Santisteban. Extensões biduais de operadores lineares e multilineares entre espaços de Riesz e reticulados de Banach. Tese (Doutorado).

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The relationship between almost Dunford-Pettis operators and almost limited operators

Cited by 5 publications

References 11 publications

Adjoints and second adjoints of almost Dunford-Pettis operators

Adjoints and second adjoints of almost Dunford-Pettis operators

Dunford–Pettis type properties and the Grothendieck property for function spaces

Extensões biduais de operadores lineares e multilineares entre espaços de Riesz e reticulados de Banach

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