Finite Representability of ℓ p -Spaces

Abstract

We are now going to switch gears and study local properties of infinite-dimensional Banach spaces. In Banach space theory the word local is used to denote finite-dimensional. We can distinguish between properties of a Banach space that are determined by its finite-dimensional subspaces and properties that require understanding of the whole space. For example, one cannot decide that a space is reflexive just by looking at its finite-dimensional subspaces, but properties like type and cotype that depend on inequalities with only finitely many vectors are local in character.