Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, II. Geometry of the Level Sets of Symbols |
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Authors: | Raul Quiroga-Barranco Nikolai Vasilevski |
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Affiliation: | (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 |
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Abstract: | In the first part [16] of this work, we described the commutative C*-algebras generated by Toeplitz operators on the unit ball whose symbols are invariant under the action of certain Abelian groups of biholomorphisms of . Now we study the geometric properties of these symbols. This allows us to prove that the behavior observed in the case of the unit disk (see [3]) admits a natural generalization to the unit ball . Furthermore we give a classification result for commutative Toeplitz operator C*-algebras in terms of geometric and “dynamic” properties of the level sets of generating symbols. This work was partially supported by CONACYT Projects 46936 and 44620, México. |
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Keywords: | Primary 47B35 Secondary 47L80, 32A36, 32M15, 53C12, 53C55 |
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