Commutants of weighted shift directed graph operator algebras

Levene, Rupert and Kribs, David and Power, Stephen Charles (2017) Commutants of weighted shift directed graph operator algebras. Proceedings of the American Mathematical Society, 145. pp. 3465-3480. ISSN 0002-9939

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Abstract

We consider non-selfadjoint operator algebras $\Lalg\lambda$ generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs~$G$. These algebras may be viewed as noncommutative generalizations of weighted Bergman space algebras, or as weighted versions of the free semigroupoid algebras of directed graphs. A complete description of the commutant is obtained together with broad conditions that ensure the double commutant property. It is also shown that the double commutant property may fail for $\Lalg{\lambda}$ in the case of the single vertex graph with two edges and a suitable choice of left weight function~$\lambda$.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the American Mathematical Society
First published in Proceedings of the American Mathematical Society in 145, 2017, published by the American Mathematical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
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ID Code:
81661
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Deposited On:
21 Sep 2016 08:30
Refereed?:
Yes
Published?:
Published