For natural numbers n ≥ 3 and r a complete description of all natural bilinear operators is presented. Next for natural numbers r and n ≥ 3 a full classification of all natural linear operators is obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-3, author = {J. Kurek and W. M. Mikulski}, title = {The natural linear operators $T* \textasciitilde\ TT^{(r)}$ }, journal = {Colloquium Mathematicae}, volume = {96}, year = {2003}, pages = {37-47}, zbl = {1020.58001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-3} }
J. Kurek; W. M. Mikulski. The natural linear operators $T* ⇝ TT^{(r)}$ . Colloquium Mathematicae, Tome 96 (2003) pp. 37-47. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-3/