Integrating representations of Banach--Lie algebras

TL;DR

This paper establishes two criteria for when representations of Banach--Lie algebras can be integrated into group representations, focusing on unbounded operators on Hilbert spaces.

Contribution

It introduces novel integrability criteria for Banach--Lie algebra representations as unbounded operators on Hilbert spaces.

Findings

Two new integrability criteria are proposed.

Criteria applicable to skew-symmetric unbounded operators.

Results facilitate the integration of Banach--Lie algebra representations.

Abstract

We give two integrability criteria for representations of Banach--Lie algebras as skew-symmetric unbounded operators on a dense domain of a Hilbert space.