Document Type
Article
Publication Date
6-1-2009
Publication Title
Indian Journal of Pure & Applied Mathematics
Abstract
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.
Repository Citation
Rajagopalan, M. and Sundaresan, K., "Generalized Shifts on Cartesian Products" (2009). Mathematics and Statistics Faculty Publications. 193.
https://engagedscholarship.csuohio.edu/scimath_facpub/193
Version
Postprint
Publisher's Statement
The final publication is available at Springer via http://dx.doi.org/10.1007/s11538-011-9662-4
Volume
40
Issue
3
