Commutants of weighted shift directed graph operator algebras
We consider non-selfadjoint operator algebras L(G,λ)\mathcal {L} (G,\lambda ) generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs GG. These algebras may be viewed as non-commutative generalizations of weighted Bergman space algebras or as weighted version...
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Veröffentlicht in: | Proceedings of the American Mathematical Society 2017-08, Vol.145 (8), p.3465-3480 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We consider non-selfadjoint operator algebras L(G,λ)\mathcal {L} (G,\lambda ) generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs GG. 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 L(G,λ)\mathfrak {L} (G,\lambda ) in the case of the single vertex graph with two edges and a suitable choice of left weight function λ\lambda. |
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ISSN: | 0002-9939 1088-6826 |
DOI: | 10.1090/proc/13477 |