Article
Operators whose adjoints are quasi p-nuclear
Author/s | Juan Manuel Delgado Sánchez
Cándido Piñeiro Gómez Enrique Serrano Aguilar |
Department | Departamento de Matemática Aplicada I |
Publication Date | 2010 |
Deposit Date | 2020-05-07 |
Abstract | For p ≥ 1, a set K in a Banach space X is said to be relatively p-compact if there exists a p-summable sequence (xn) in X with K ⊆{Pn αnxn : (αn) ∈ B`p0}. We prove that an operator T : X → Y is p-compact (i.e., T maps ... For p ≥ 1, a set K in a Banach space X is said to be relatively p-compact if there exists a p-summable sequence (xn) in X with K ⊆{Pn αnxn : (αn) ∈ B`p0}. We prove that an operator T : X → Y is p-compact (i.e., T maps bounded sets to relatively p-compact sets) iff T∗ is quasi p-nuclear. Further, we characterize p-summing operators as those operators whose adjoints map relatively compact sets to relatively p-compact sets. |
Citation | Juan Manuel Delgado Sánchez, , Cándido Piñeiro Gómez, y Enrique Serrano Aguilar, (2010). Operators whose adjoints are quasi p-nuclear. Studia Mathematica, 197 (3), 291-304. |
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