Stampacchia's property, self-duality and orthogonality relations

Details Stampacchia's property, self-duality and orthogonality relations Stampacchia's property, self-duality and orthogonality relations

2010-08-29

arxiv.org/abs/1008.4958v1

Mathematics

Functional Analysis

Scientific paper

We show that if the conclusion of the well known Stampacchia Theorem, on variational inequalities, holds on a Banach space X, then X is isomorphic to a Hilbert space. Motivated by this we obtain a relevant result concerning self-dual Banach spaces and investigate some connections between existing notions of orthogonality and self-duality. Moreover, we revisit the notion of the cosine of a linear operator and show that it can be used to characterize Hilbert space structure. Finally, we present some consequences of our results to quadratic forms and to evolution triples.

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