A sequence (xn) in a Banach space X is said to be weakly-p-summable, 1 ≤ p < ∞, when for each x* ∈ X*, (x*xn) ∈ lp. We shall say that a sequence (xn) is weakly-p-convergent if for some x ∈ X, (xn - x) is weakly-p-summable.
@article{urn:eudml:doc:39899,
title = {Absolutely ($\infty$,p) summing and weakly-p-compact operators in Banach spaces.},
journal = {Extracta Mathematicae},
volume = {5},
year = {1990},
pages = {153-155},
zbl = {0744.47015},
mrnumber = {MR1125690},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39899}
}
Fernández Castillo, Jesús M. Absolutely (∞,p) summing and weakly-p-compact operators in Banach spaces.. Extracta Mathematicae, Tome 5 (1990) pp. 153-155. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39899/