Relative Positions of Half-sided Modular Inclusions

Fuente: arXiv
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Autore principale: Koot, Ian
Natura: Preprint
Pubblicazione: 2025
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author Koot, Ian
author_facet Koot, Ian
contents Let $K_1 \subset H$ and $K_2 \subset H$ be half-sided modular inclusions in a common standard subspace $H$. We prove that the inclusion $K_1 \subset K_2$ holds if and only if we have an inclusion of spectral subspaces of the generators of the positive one-parameter groups associated to the half-sided modular inclusions $K_1 \subset H$ and $K_2 \subset H$. From this we give a characterization of this situation in terms of (operator valued) symmetric inner functions. We illustrate these characterizations with some examples of non-trivial phenomena occurring in this setting.
format Preprint
id arxiv_https___arxiv_org_abs_2503_18036
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Relative Positions of Half-sided Modular Inclusions
Koot, Ian
Mathematical Physics
Operator Algebras
Let $K_1 \subset H$ and $K_2 \subset H$ be half-sided modular inclusions in a common standard subspace $H$. We prove that the inclusion $K_1 \subset K_2$ holds if and only if we have an inclusion of spectral subspaces of the generators of the positive one-parameter groups associated to the half-sided modular inclusions $K_1 \subset H$ and $K_2 \subset H$. From this we give a characterization of this situation in terms of (operator valued) symmetric inner functions. We illustrate these characterizations with some examples of non-trivial phenomena occurring in this setting.
title Relative Positions of Half-sided Modular Inclusions
topic Mathematical Physics
Operator Algebras
url https://arxiv.org/abs/2503.18036