On a characteristic property of finite-dimensional Banach spaces

Abstract

This paper is inspired by a counterexample of J. Kurzweil, whose intention was to demonstrate that a certain property of linear operators on finite-dimensional spaces need not be preserved in infinite dimension.

We obtain a stronger result, which says that no infinite-dimensional Banach space can have the given property. Along the way, we will also derive an interesting proposition related to Dvoretzky's theorem.

Keywords

• norm inequality
• product integration
• Dvoretzky's theorem