Indian Journal of Pure & Applied Mathematics
It is proved that if E, F are infinite dimensional strictly convex Banach spaces totally incomparable in a restricted sense, then the Cartesian product E×F with the sum or sup norm does not admit a forward shift. As a corollary it is deduced that there are no backward or forward shifts on the Cartesian product`p1×`p2,1< p16=p2<∞, with the supremum norm thus settling a problem left open in Rajagopalan and Sundaresan in J. Analysis 7 (1999(, 75-81 and also a problem stated as unsolved in Rassias and Sundaresan.
Rajagopalan, M. and Sundaresan, K., "Generalized Shifts on Cartesian Products" (2009). Mathematics Faculty Publications. 193.
The final publication is available at Springer via http://dx.doi.org/10.1007/s11538-011-9662-4