Commutants of weighted shift directed graph operator algebras
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- by David W. Kribs, Rupert H. Levene and Stephen C. Power PDF
- Proc. Amer. Math. Soc. 145 (2017), 3465-3480 Request permission
Abstract:
We consider non-selfadjoint operator algebras $\mathcal {L} (G,\lambda )$ generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs $G$. These algebras may be viewed as non-commutative 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 $\mathfrak {L} (G,\lambda )$ in the case of the single vertex graph with two edges and a suitable choice of left weight function $\lambda$.References
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Additional Information
- David W. Kribs
- Affiliation: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1
- Rupert H. Levene
- Affiliation: School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
- MR Author ID: 728402
- Stephen C. Power
- Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster, United Kingdom, LA1 4YF
- MR Author ID: 141635
- Received by editor(s): May 24, 2016
- Received by editor(s) in revised form: September 12, 2016, and September 14, 2016
- Published electronically: February 21, 2017
- Communicated by: Adrian Ioana
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3465-3480
- MSC (2010): Primary 47L75, 47L55, 47B37
- DOI: https://doi.org/10.1090/proc/13477
- MathSciNet review: 3652799