Infimal convolution in Efimov–Steˇckin Banach spaces

Let (X, · ) be a reflexive Banach space with Kadec–Klee norm. Let f : X→(−∞,+∞] be a function which is either Lipschitzian or is proper, bounded below, and lower semi-continuous. Then f is supported from below by residually many parabolas opening downward, that is, the infimal convolution of · 2 and f is attained at residually many points of X. © 2007 Elsevier Inc. All rights reserved