First steps in the geography of scale Hilbert structures

TL;DR

This paper introduces an invariant for scale Hilbert spaces to distinguish large classes of these structures, advancing the understanding of their classification.

Contribution

It defines a new invariant for scale Hilbert spaces and demonstrates its effectiveness in differentiating classes up to scale isomorphism.

Findings

The invariant successfully distinguishes large classes of scale Hilbert spaces.

It provides a new tool for the classification of scale structures.

The approach advances the theoretical understanding of scale Hilbert space geometry.

Abstract

Scale structures were introduced by H.Hofer, K.Wysocki, and E.Zehnder. In this note we define an invariant for scale Hilbert spaces modulo scale isomorphism and use it to distinguish large classes of scale Hilbert spaces.