Journal of Operator Theory

Volume 93, Issue 2, Spring 2025 pp. 315-354.

Noncommutative domains, universal operator models, and operator algebras. II

Authors: Gelu Popescu
Author institution: Department of Mathematics, The University of Texas at San Antonio, San Antonio, TX 78249, U.S.A.

Summary: In a recent paper, we introduced and studied the class of admissible noncommutative domains $\mathcal D_{g^{-1}}(\mathcal H)$ in $B(\mathcal H)^n$. Each such a domain admits a universal model ${\bf W}:=(W_1,\ldots, W_n)$ of weighted left creation operators acting on the full Fock space. In the present paper, we obtain a Beurling type characterization of the invariant subspaces of the universal model ${\bf W}$ and develop a dilation theory for the elements of the domain $\mathcal D_{g^{-1}}(\mathcal H)$. We also obtain results concerning the commutant lifting and Toeplitz-corona in our setting as as well as some results on the boundary property for universal models.

DOI: http://dx.doi.org/10.7900/jot.2023mar02.2408
Keywords: noncommutative domains, universal operator models, Fock spaces, invariant subspaces, dilation theory, commutant lifting, Toeplitz-corona theorem, boundary representation

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