Operators whose adjoints are quasi p-nuclear

Delgado J.M. Piñeiro C. Serrano E.
Studia Mathematica
Doi 10.4064/sm197-3-6
Volumen 197 páginas 291 - 304
2010-06-14
Citas: 49
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 ? {?n?nxn: (?n) ? Blp,}. 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. © Instytut Matematyczny PAN, 2010.
P-compact operator, P-compact sets, P-nuclear operator, P-summing operator, Quasi p-nuclear operator, Weakly p-compact operator
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