SL(n) covariant matrix-valued valuations on Orlicz spaces

TL;DR

This paper classifies all continuous SL(n) covariant valuations on Orlicz spaces, revealing that the moment matrix is unique in dimensions three and higher, with a new functional emerging in dimension two.

Contribution

It provides a complete classification of SL(n) covariant valuations on Orlicz spaces without symmetry assumptions, identifying the moment matrix as unique in higher dimensions.

Findings

Moment matrix is the only valuation for n ≥ 3.

A new functional appears in dimension two.

Complete classification of valuations without symmetry assumptions.

Abstract

All continuous, SL(n) covariant valuations on Orlicz spaces are completely classified without any symmetric assumptions. It is shown that the moment matrix is the only such valuation if n\geq3, while a new functional shows up in dimension two.