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arXiv · 2606.25395

Wold-type decomposition and Beurling-Type Theorem for Covariant Representations

Dimple Saini·Azad Rohilla
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Abstract

Using operator inequalities, we study a Wold-type decomposition of covariant representations. Building on this decomposition, we prove a Beurling-type theorem showing that every nonzero invariant subspace is uniquely determined by its wandering subspace. Our results extend classical theorems of Beurling and subsequent developments for left-invertible operators to the setting of covariant representations of $C^*$-correspondences, providing a unified framework for invariant subspace theory under operator inequalities.

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Dimple Saini, Azad Rohilla. 2026-06-24. Wold-type decomposition and Beurling-Type Theorem for Covariant Representations. https://arxiv.org/abs/2606.25395

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