Legendre forms are used in the literature for second-order sufficient optimality conditions of optimization problems in (reflexive) Banach spaces. We show that if a Legendre form exists on a reflexive Banach space, then this space is already isomorphic to a Hilbert space.
Cite this article
Felix Harder, Legendre Forms in Reflexive Banach Spaces. Z. Anal. Anwend. 37 (2018), no. 4, pp. 377–388DOI 10.4171/ZAA/1619