COMMUTANTS OF WEIGHTED SHIFT DIRECTED GRAPH OPERATOR ALGEBRAS

被引：4
|
作者：
Kribs, David W. [1 ]
Levene, Rupert H. [2 ]
Power, Stephen C. [3 ]
机构：
[1] Univ Guelph, Dept Math & Stat, Guelph, ON, Canada
[2] Univ Coll Dublin, Sch Math & Stat, Dublin 4, Ireland
[3] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 08期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Directed graph; weighted shift; non-selfadjoint algebra; commutant; left regular representation; creation operators; Fock space; REFLEXIVITY;
D O I：
10.1090/proc/13477
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider non-selfadjoint operator algebras L(G,lambda) generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs G lambda 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,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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页码：3465 / 3480
页数：16
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