A nonlinear map for midpoint locally uniformly rotund renorming

S. Lajara, A.J. Pallars
2005 Bulletin of the Australian Mathematical Society  
We provide a criterion for midpoint locally uniformly rotund renormability of normed spaces involving the class of σ-slicely continuous maps, recently introduced by Moltó, Orihuela, Troyanski and Valdiva in 2003. As a consequence of this result, we obtain a theorem of G. Alexandrov concerning the three space problem for midpoint locally uniformly rotund renormings of Banach spaces.
doi:10.1017/s0004972700034857 fatcat:b6xvqntqszc5vmumcpwn3nvleu