Characterising subspaces of Banach spaces with a Schauder basis having the shift property

TL;DR

This paper characterizes certain subspaces of Banach spaces with a Schauder basis that exhibit the shift property, focusing on embeddings into spaces with unconditional bases where block sequences are equivalent.

Contribution

It provides an intrinsic characterization of separable reflexive Banach spaces that embed into spaces with an unconditional basis and the shift property, using methods from Odell and Schlumprecht.

Findings

Characterization of Banach spaces with the shift property

Embedding criteria for reflexive Banach spaces

Application of Odell and Schlumprecht methods

Abstract

We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of E. Odell and T. Schlumprecht.