Identificador persistente para citar o vincular este elemento: http://hdl.handle.net/10662/10181
Títulos: The ξ ,ς -Dunford Pettis property
Autores/as: Causey, R.M.
Palabras clave: Completely continuous operators;Schur property;Dunford Pettis property;Operator ideals;Ordinal ranks;Operadores completamente continuos;Propiedad Schur;Propiedad Dunford Pettis;Ideales de operador;Filas ordinales
Fecha de publicación: 2019
Editor/a: Universidad de Extremadura
Resumen: Using the hierarchy of weakly null sequences introduced in [2], we introduce two new families of operator classes. The first family simultaneously generalizes the completely continuous operators and the weak Banach-Saks operators. The second family generalizes the class DP. We study the distinctness of these classes, and prove that each class is an operator ideal. We also investigate the properties possessed by each class, such as injectivity, surjectivity, and identification of the dual class. We produce a number of examples, including the higher ordinal Schreier and Baernstein spaces. We prove ordinal analogues of several known results for Banach spaces with the Dunford-Pettis, hereditary Dunford-Pettis property, and hereditary by quotients Dunford-Pettis property. For example, we prove that for any 0 ≤ ξ , ς < ω₁, a Banach space X has the hereditary ω^ξ; ω^ς-Dunford Pettis property if and only if every seminormalized, weakly null sequence either has a subsequence which is an l_₁^( ω^ξ ) -spreading model or a c_₀^(ω^ς ) -spreading model.
URI: http://hdl.handle.net/10662/10181
DOI: 10.17398/2605-5686.34.2.135
Colección:Extracta Mathematicae Vol. 34, nº 2 (2019)

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