Chapter

Topics in Operator Theory

Volume 202 of the series Operator Theory: Advances and Applications pp 553-568

Parabolic Quasi-radial Quasi-homogeneous Symbols and Commutative Algebras of Toeplitz Operators

  • Nikolai VasilevskiAffiliated withDepartamento de Matemáticas, CINVESTAV

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Abstract

We describe new Banach (not C* !) algebras generated by Toeplitz operators which are commutative on each weighted Bergman space over the unit ball \( \mathbb{B}^n \), where n > 2. For n = 2 all these algebras collapse to the single C*-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.

Keywords

Toeplitz operator weighted Bergman space commutative Banach algebra parabolic quasi-radial quasi-homogeneous symbol

Mathematics Subject Classification (2000)

Primary 47B35 Secondary 47L80 32A36