Strong factorization of ultradifferentiable vectors associated with compact Lie group representations

TL;DR

This paper proves a strong factorization theorem for ultradifferentiable vectors in compact Lie group representations, confirming a conjecture for analytic vectors and advancing understanding of their structure.

Contribution

It establishes a Dixmier-Malliavin type factorization theorem for ultradifferentiable vectors, solving a conjecture for analytic vectors in compact Lie groups.

Findings

Proves a strong factorization theorem for ultradifferentiable vectors.

Confirms a conjecture for analytic vectors in compact Lie groups.

Advances the theory of vector factorization in representation spaces.

Abstract

We show a strong factorization theorem of Dixmier-Malliavin type for ultradifferentiable vectors associated with compact Lie group representations on sequentially complete locally convex Hausdorff spaces. In particular, this solves a conjecture by Gimperlein et al. [J. Funct. Anal. 262 (2012), 667-681] for analytic vectors in the case of compact Lie groups.