HOLOMORPHIC EXTENSION OF ONE-PARAMETER OPERATOR GROUPS

Beltitä D, Neeb KH (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Pure and Applied Functional Analysis Yokohama Publishers

Book Volume: 9

Pages Range: 1483-1526

Journal Issue: 6

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.

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

"Gheorghe Mihoc - Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy RO Romania (RO)

How to cite

APA:

Beltitä, D., & Neeb, K.H. (2024). HOLOMORPHIC EXTENSION OF ONE-PARAMETER OPERATOR GROUPS. Pure and Applied Functional Analysis, 9(6), 1483-1526.

MLA:

Beltitä, Daniel, and Karl Hermann Neeb. "HOLOMORPHIC EXTENSION OF ONE-PARAMETER OPERATOR GROUPS." Pure and Applied Functional Analysis 9.6 (2024): 1483-1526.

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