Holomorphic extension of one-parameter operator groups

2023/04/19 by Daniel Beltiţă, Beltita, Daniel, Karl‐Hermann Neeb +1 · 1 citation
Mathematics · #47D06 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Primary 22E45 #Representation Theory (math.RT) #Secondary 46A20

paper · pdf · doi:10.48550/arxiv.2304.09597

openalex publication_date 2023/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study holomorphic extensions of one-parameter groups on locally convex spaces with a view to applications to KMS boundary conditions. In the first part we deal with analytic extensions of one-parameter groups of operators on locally convex spaces and in the second part we apply our results to spaces of distribution vectors of unitary representations of Lie groups. This leads to new tools that can be used to construct, from unitary Lie group representations, nets of standard subspaces, as they appear in Algebraic Quantum Field Theory. We also show that these methods fail for spaces of analytic vectors, and this in turn leads to new maximality results for domains of analytic extensions of orbit maps for unitary representations.

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• Crowned Lie groups and nets of real subspaces

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