Remarks on the set of norm-attaining functionals and differentiability

[EN] We use the smooth variational principle and a standard renorming to give a short direct proof of the classical Bishop-Phelps-Bollobas theorem on the density of norm-attaining functionals for weakly compactly generated Banach spaces. Then we show that a slight adjustment of a known Preiss-Zajfcek differentiability argument provides a simple, useful characterization of individual norms on separable Banach spaces admitting residual sets of norm-attaining functionals in terms of Frechet differentiability of their dual norms.This research was partly supported by MICINN and FEDER Projects MTM2014-57838-C2-1-P, MTM2014-57838-C2-2-P. The first named author was also partly supported by Fundacion Seneca, Region de Murcia grant 19368/PI/14.Guirao Sánchez, AJ.; Montesinos Santalucia, V.; Zizler, V. (2018). Remarks on the set of norm-attaining functionals and differentiability. Studia Mathematica. 241(1):71-86. doi:10.4064/sm8768-6-2017S7186241