Relative Positions of Half-sided Modular Inclusions

Koot I (2025)

Publication Language: English

Publication Status: In review

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

URI: https://arxiv.org/abs/2503.18036

Abstract

Let K1⊂H and K2⊂H be half-sided modular inclusions in a common standard subspace H. We prove that the inclusion K1⊂K2 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 K1⊂H and K2⊂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.

Authors with CRIS profile

Ian Koot Lehrstuhl für Mathematik (Operatoralgebren) (Heisenberg-Professur)

How to cite

APA:

Koot, I. (2025). Relative Positions of Half-sided Modular Inclusions. (Unpublished, In review).

MLA:

Koot, Ian. Relative Positions of Half-sided Modular Inclusions. Unpublished, In review. 2025.

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