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arXiv · 2503.18036

Relative Positions of Half-sided Modular Inclusions

Ian Koot
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Abstract

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.

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Ian Koot. 2025-03-23. Relative Positions of Half-sided Modular Inclusions. https://arxiv.org/abs/2503.18036

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