On nonexistence of strongly unique best approximations
The author proves the following theorems: If M is an n-dimensional subspace of a real normed linear space X and if \(x\in X\setminus M\) and \(m\in M\) are such that \(\dim F(x-m)\leq n\) (where \(F(z)=\{f\in X^*:\quad \| f\| =1,\quad f(z)=\| z\| \}),\) then m is not a strongly unique best approximation in M to x. If there is a \(z\neq 0\) in a real normed linear space x such that dim F(z)\(=n\), then there exists an n- dimensional space M of X, an element \(x\in X\setminus M\), and a strongly unique best approximation m in M to x.
scientific article; zbMATH DE number 4129394