On a norming property of subspaces of a Banach space and some applications (Q6593270)

Let \(X\) be a real Banach space. The authors continue their work on the linear structure of the set of norm-preserving extensions from a subspace \(Y \subset X\). \(Y\) is said to be \(m\)-heavy if this set of extensions contains an \(m\)-dimensional subspace \(M \subset X^\ast\). Theorem~3.5 gives an equivalent condition: in terms of canonical identification of the quotient space \(X^\ast/Y^\bot\) with \(Y^\ast\), \(M\) gets isometrically embedded into \(Y^\ast\).