A property of infinite-dimensional Hilbert spaces
type: Item
instance of: scholarly article
title: A property of infinite-dimensional Hilbert spaces
zbMATH Open document ID: 0676.46015
DOI: 10.1016/0022-247X(89)90112-1
author: Michele Frasca
author: Alfonso Villani
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: 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.
reviewed by: A.Donescu
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 49J40
zbMATH DE Number: 4107445
zbMATH Keywords: pseudo-atom
zbMATH Keywords: variational inequalities
MaRDI profile type: Publication
cites work: Q4606219
cites work: An extension of Tietze's theorem
cites work: Some Topological Properties of Convex Sets
cites work: Q5676645
cites work: Q3744774
description: scientific article; zbMATH DE number 4107445