Parabolic Quasi-radial Quasi-homogeneous Symbols and Commutative Algebras of Toeplitz Operators
Parabolic Quasi-radial Quasi-homogeneous Symbols and Commutative Algebras of Toeplitz Operators
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DOI：
10.1007/978-3-0346-0158-0_33
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发表时间：
2010
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影响因子：
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通讯作者：
N. Vasilevski
中科院分区：
文献类型：
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作者：
N. Vasilevski
我们描述了新的Banach(NOTC*！)单位球上每个加权Bergman空间上可交换的Toeplitz算子生成的代数，其中>；2.Forn=2.所有这些代数都折叠成由具有拟抛物符号的Toeplitz算子生成的单C*-代数.作为副产品，我们描述了相互交换的Toeplitz算子的乘积本身是Toeplitz算子的情形。
We describe new Banach (notC* !) algebras generated by Toeplitz operators which are commutative on each weighted Bergman space over the unit ball, wheren> 2. Forn= 2 all these algebras collapse to the singleC*-algebra generated by Toeplitz operators with quasi-parabolic symbols. As a by-product, we describe the situations when the product of mutually commuting Toeplitz operators is a Toeplitz operator itself.