Generalized Shifts on Cartesian Products
نویسنده
چکیده
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 < p1 6= 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, J. Math. Anal. Applications (260)(2001), 36-45.
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تاریخ انتشار 2009