Functional analytic background for a theory of infinite-dimensional reductive Lie groups

TL;DR

This paper explores the functional analytic foundations necessary for understanding infinite-dimensional reductive Lie groups, focusing on operator theory, ideals, and amenability to support their representation theory.

Contribution

It introduces key functional analytic concepts such as norm ideals, triangular integrals, and operator factorizations tailored for infinite-dimensional reductive Lie groups.

Findings

Development of a framework for Banach-Lie group representation theory

Analysis of operator factorizations in infinite dimensions

Insights into amenability and triangular integrals in this context

Abstract

Motivated by the interesting and yet scattered developments in representation theory of Banach-Lie groups, we discuss several functional analytic issues which should underlie the notion of infinite-dimensional reductive Lie group: norm ideals, triangular integrals, operator factorizations, and amenability.