A counterexample to a strengthening of a question of V. D. Milman

Abstract

. — Let | · | be the standard Euclidean norm on R n and let X = ( R n , ∥ · ∥ ) be a normed space. A subspace Y ⊂ X is strongly α -Euclidean if there is a constant t such that t | y | ⩽ ∥ y ∥ ⩽ αt | y | for every y ∈ Y