Commutants of weighted shift directed graph operator algebras

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Title: Commutants of weighted shift directed graph operator algebras
Authors: Kribs, David W.
Levene, Rupert H.
Power, Stephen C.
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Date: Aug-2017
Online since: 2018-04-25T16:46:05Z
Abstract: We consider non-selfadjoint operator algebras L(G, λ) 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 L(G, λ) in the case of the single vertex graph with two edges and a suitable choice of left weight function λ.
Type of material: Journal Article
Publisher: American Mathematical Society
Journal: Proceedings of the American Mathematical Society
Volume: 145
Issue: 8
Start page: 3465
End page: 3480
Copyright (published version): 2017 American Mathematical Society
Keywords: Directed graphWeighted shiftNon-selfadjoint algebraCommutantLeft regular representationCreation operatorsFock space
DOI: 10.1090/proc/13477
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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