We prove that the symmetric convexified Tsirelson space is of weak cotype 2 but not of cotype 2.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-1-1, author = {Peter G. Casazza and Niels J. Nielsen}, title = {A Banach space with a symmetric basis which is of weak cotype 2 but not of cotype 2}, journal = {Studia Mathematica}, volume = {157}, year = {2003}, pages = {1-16}, zbl = {1032.46011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-1-1} }
Peter G. Casazza; Niels J. Nielsen. A Banach space with a symmetric basis which is of weak cotype 2 but not of cotype 2. Studia Mathematica, Tome 157 (2003) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-1-1/