Commutative <Emphasis Type="Italic">C</Emphasis>*-Algebras of Toeplitz Operators on the Unit Ball,I. Bargmann-Type Transforms and Spectral Representations of Toeplitz Operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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*Commutative <Emphasis Type="Italic">C</Emphasis>-Algebras of Toeplitz Operators on the Unit Ball,I. Bargmann-Type Transforms and Spectral Representations of Toeplitz Operators**

Authors:	Raul Quiroga-Barranco Nikolai Vasilevski

Institution:	(1) Centro de Investigación en Matemáticas, Apartado Postal 402, 36000 Guanajuato, Gto., México;(2) Departamento de Matemáticas, CINVESTAV, Apartado Postal 14-740, 07000 México, D.F., México

Abstract:	Extending known results for the unit disk, we prove that for the unit ball ${\mathbb{B}}^n$ there exist n+2 different cases of commutative C*-algebras generated by Toeplitz operators, acting on weighted Bergman spaces. In all cases the bounded measurable symbols of Toeplitz operators are invariant under the action of certain commutative subgroups of biholomorphisms of the unit ball. This work was partially supported by CONACYT Projects 46936 and 44620, México.

Keywords:	Primary 47B35 Secondary 47L80 32A36
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