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**Rights statement:**First published in Proceedings of the American Mathematical Society in 145, 2017, published by the American Mathematical SocietyAccepted author manuscript, 362 KB, PDF document

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- http://www.ams.org/journals/proc/0000-000-00/S0002-9939-2017-13477-7/home.html
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Research output: Contribution to journal › Journal article › peer-review

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**Commutants of weighted shift directed graph operator algebras.** / Levene, Rupert; Kribs, David; Power, Stephen Charles.

Research output: Contribution to journal › Journal article › peer-review

Levene, R, Kribs, D & Power, SC 2017, 'Commutants of weighted shift directed graph operator algebras', *Proceedings of the American Mathematical Society*, vol. 145, pp. 3465-3480. https://doi.org/10.1090/proc/13477

Levene, R., Kribs, D., & Power, S. C. (2017). Commutants of weighted shift directed graph operator algebras. *Proceedings of the American Mathematical Society*, *145*, 3465-3480. https://doi.org/10.1090/proc/13477

Levene R, Kribs D, Power SC. Commutants of weighted shift directed graph operator algebras. Proceedings of the American Mathematical Society. 2017;145:3465-3480. https://doi.org/10.1090/proc/13477

@article{24e046b404ea48899eb569b52e290b59,

title = "Commutants of weighted shift directed graph operator algebras",

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~$\lambda$.",

keywords = "Directed graph, weighted shift, non-selfadjoint algebra, commutant, left regular representation, creation operators, Fock space",

author = "Rupert Levene and David Kribs and Power, {Stephen Charles}",

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

year = "2017",

doi = "10.1090/proc/13477",

language = "English",

volume = "145",

pages = "3465--3480",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Commutants of weighted shift directed graph operator algebras

AU - Levene, Rupert

AU - Kribs, David

AU - Power, Stephen Charles

N1 - First published in Proceedings of the American Mathematical Society in 145, 2017, published by the American Mathematical Society

PY - 2017

Y1 - 2017

N2 - 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~$\lambda$.

AB - 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~$\lambda$.

KW - Directed graph

KW - weighted shift

KW - non-selfadjoint algebra

KW - commutant

KW - left regular representation

KW - creation operators

KW - Fock space

U2 - 10.1090/proc/13477

DO - 10.1090/proc/13477

M3 - Journal article

VL - 145

SP - 3465

EP - 3480

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -