Finite extremal characterization of strong uniqueness in normed spaces (Q809298)

For an n-dimensional (n\(\geq 1)\) subspace M of a normed space X, an element \(m\in M\) is called a strongly unique best approximation (SUBA) in M to \(x\in X\setminus M\) if there exists \(c>0\) such that \(\| x-m\| \leq \| x-y\| -c\| m-y\|,\) for all \(y\in M\). The aim of this paper is to give characterizations of a SUBA in terms of a finite number (\(\leq 2n)\) of extremal elements of the unit ball \(B(X^*)\) of the conjugate space \(X^*\). Characterizations of SUBA in terms of the extremal elements of B(X) were first given by D. E. Wulbert. The obtained results are applied to the space C(T) and to finite dimensional interpolating subspaces of a normed space.