Quasi-Radial Quasi-Homogeneous Symbols and Commutative Banach Algebras of Toeplitz Operators

被引：37
作者：
Vasilevski, Nikolai [1 ]
机构：
[1] CINVESTAV, Dept Matemat, Mexico City 07000, DF, Mexico
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2010年 / 66卷 / 01期
关键词：
Toeplitz operator; weighted Bergman space; commutative Banach algebra; quasi-radial quasi-homogeneous symbol; C-ASTERISK-ALGEBRAS; UNIT BALL;
D O I：
10.1007/s00020-009-1732-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present here a quite unexpected result: Apart from already known commutative C*-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C*-algebra, and for n = 1 all of them collapse to the algebra generated by Toeplitz operators with radial symbols.
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收藏
页码：141 / 152
页数：12
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