A property of infinite-dimensional Hilbert spaces
Let H be an infinite-dimensional Hilbert space and let B be a closed ball of H. Then there is an affine continuous function T: \(H\to H\), for which \(<T(x),x>\) is an interior point of \(\{<T(x),u>:\) \(u\in B\}\), (\(\forall)x\in B\). This results from a stronger theorem, which is proved in this work. After proving the theorems relating to the above property, the authors give an example that shows that a conjecture of B. Ricceri, which says that an assumption of a theorem for variational inequalities cannot be weakened, is a true one.
scientific article; zbMATH DE number 4107445