Journal of Operator Theory

Volume 66, Issue 2, Fall 2011 pp. 425-450.

Isomorphisms of non-commutative domain algebras

Authors: Alvaro Arias (1) and Frederic Latremoliere (2)
Author institution: (1) Department of Mathematics, University of Denver, Denver, CO 80208, USA
(2) Department of Mathematics, University of Denver, Denver, CO 80208, USA

Summary: Noncommutative domain algebras were introduced by Popescu as the non-selfadjoint operator algebras generated by weighted shifts on the Full Fock space. This paper uses results from several complex variables to classify many noncommutative domain algebras, and it uses results from operator theory to obtain new bounded domains in $\mathbb{C}^{n}$ with non-compact automorphic group.

Keywords: non-self-adjoint operator algebras, disk algebra, weighted shifts, biholomorphic domains, circular domains

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