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 . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-6,
author = {J. M. Delgado and C. Pi\~neiro and E. Serrano},
title = {Operators whose adjoints are quasi p-nuclear},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {291-304},
zbl = {1190.47024},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-6}
}
J. M. Delgado; C. Piñeiro; E. Serrano. Operators whose adjoints are quasi p-nuclear. Studia Mathematica, Tome 196 (2010) pp. 291-304. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-3-6/