On the structure of asymptotic l_p spaces

TL;DR

This paper demonstrates that separable, reflexive asymptotic l_p spaces can be embedded into reflexive spaces with an asymptotic l_p finite-dimensional decomposition, providing an intrinsic characterization of their subspaces.

Contribution

It establishes a new embedding result for asymptotic l_p spaces into spaces with an asymptotic l_p FDD, advancing the structural understanding of these spaces.

Findings

Separable, reflexive asymptotic l_p spaces embed into reflexive spaces with an asymptotic l_p FDD.

Provides an intrinsic characterization of subspaces of spaces with an asymptotic l_p FDD.

Generalizes previous results on the structure of asymptotic l_p spaces.

Abstract

We prove that if X is a separable, reflexive space which is asymptotic l_p, then X embeds into a reflexive space Z having an asymptotic l_p finite-dimensional decomposition. This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic l_p FDD. More general results of this type are also obtained.