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Zeitschrift für Analysis und ihre Anwendungen

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Volume 37, Issue 4, 2018, pp. 377–388
DOI: 10.4171/ZAA/1619

Published online: 2018-10-18

Legendre Forms in Reflexive Banach Spaces

Felix Harder[1]

(1) Brandenburgische Technische Universität Cottbus, Germany

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.

Keywords: Legendre form, second-order optimality conditions, Hilbertizable space, quadratic form, coercive bilinear form

Harder Felix: Legendre Forms in Reflexive Banach Spaces. Z. Anal. Anwend. 37 (2018), 377-388. doi: 10.4171/ZAA/1619