Petr Hájek, Michal Johanis, Smooth Analysis in Banach Spaces, De Gruyter Series in Nonlinear Analysis and Applications, Vol. 19, xvi + 465 pp, Walter de Gruyter, Berlin - New York, 2014, ISBN: 978-3-11-025898-1, e-ISBN: 978-3-11-025899-8, ISSN: 0941-813X - COBZAȘ, S. (Studia Universitatis Babeș-Bolyai Mathematica, 2015)
Smoothness is one of the most important and most studied topic in both finite and infinite dimensional analysis. It turns out that in the infinite dimensional case the existence and the properties of smooth mappings between Banach spaces are tightly interconnected withy the structural properties of the underlying spaces. In some cases the existence of a smooth norm forces the Banach space to be isomorphic to a Hilbert one.