For a Banach space X, we show how the existence of a norm-one element u in X and a norm-one continuous bilinear mapping f: X x X --> X satisfying f(x,u) = f(u,x) = x for all x in X, together with some more intrinsic conditions, can be utilized to characterize X as a member of some relevant subclass of the class of Banach spaces.
@article{urn:eudml:doc:44216,
title = {Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {9},
year = {1996},
pages = {149-189},
zbl = {0872.46017},
mrnumber = {MR1435782},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44216}
}
Rodríguez Palacios, A. Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 9 (1996) pp. 149-189. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44216/