Bergman Space Structure,Commutative Algebras of Toeplitz Operators,and Hyperbolic Geometry |
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Authors: | NL Vasilevski |
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Institution: | (1) Departamento de Matemáticas, CINVESTAV-IPN, A.P. 14-740, México, D.F. 07000, México. E-mail: nvasilev@math.cinvestav.mx, MX |
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Abstract: | We exhibit a surprising but natural connection among the Bergman
space structure, commutative algebras of Toeplitz operators and pencils of
hyperbolic straight lines. The commutative C*-algebras of Toeplitz operators
on the unit disk can be classified as follows. Each pencil of hyperbolic straight
lines determines the set of symbols consisting of functions which are constant
on corresponding cycles, the orthogonal trajectories to lines forming a pencil.
It turns out that the C*-algebra generated by Toeplitz operators with this
class of symbols is commutative.
Submitted: January 15, 2001?Revised: February 7, 2002 |
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Keywords: | Mathematics Subject Classification (2000) Primary 47B35 Secondary 47E20 30C ? Toeplitz operators Bergman space hyperbolic geometry |
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