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Mathematics and Statistics Faculty Publications
Generalized shifts; backward shifts; forward shifts; Cartesian products; subspaces; Banach spaces; strictly convex; totally incomparable; isometrically incomparable;reflexive Banach spaces
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Generalized Shifts On Cartesian Products, M. Rajagopalan, K. Sundaresan
Generalized Shifts On Cartesian Products, M. Rajagopalan, K. Sundaresan
Mathematics and Statistics Faculty Publications
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.