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arXiv · 2301.05947

Beurling quotient subspaces for covariant representations of product systems

Azad Rohilla·Harsh Trivedi·Shankar Veerabathiran
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Abstract

We characterize Beurling quotient subspaces for pure doubly commuting isometric representations of product systems. As a consequence, we derive a concrete regular dilation theorem for a pure completely contractive covariant representation which satisfies Brehmer-Solel condition and using it and the above characterization, we provide a necessary and sufficient condition that when a completely contractive covariant representation is unitarily equivalent to the compression of the induced representation on the Beurling quotient subspace. Further, we study the relation between Sz.Nagy-Foias type factorization of isometric multi-analytic operators and joint invariant subspaces.

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Azad Rohilla, Harsh Trivedi, Shankar Veerabathiran. 2023-09-13. Beurling quotient subspaces for covariant representations of product systems. https://doi.org/10.1007/s43034-023-00301-0

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