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    Rights statement: First published in Proceedings of the American Mathematical Society in 145, 2017, published by the American Mathematical Society

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    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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Commutants of weighted shift directed graph operator algebras

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<mark>Journal publication date</mark>2017
<mark>Journal</mark>Proceedings of the American Mathematical Society
Volume145
Number of pages16
Pages (from-to)3465-3480
Publication StatusPublished
Early online date21/02/17
<mark>Original language</mark>English

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~$\lambda$.

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First published in Proceedings of the American Mathematical Society in 145, 2017, published by the American Mathematical Society