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/