It is shown that for every k ∈ ℕ and every spreading sequence eₙₙ that generates a uniformly convex Banach space E, there exists a uniformly convex Banach space admitting eₙₙ as a k+1-iterated spreading model, but not as a k-iterated one.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-1-4, author = {Spiros A. Argyros and Pavlos Motakis}, title = {Examples of k-iterated spreading models}, journal = {Studia Mathematica}, volume = {215}, year = {2013}, pages = {57-78}, zbl = {1295.46010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-1-4} }
Spiros A. Argyros; Pavlos Motakis. Examples of k-iterated spreading models. Studia Mathematica, Tome 215 (2013) pp. 57-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm217-1-4/