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
This work was partially supported by CONACYT Project 80503, México.
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Communicated by I.M. Spitkovsky.
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© 2010 Birkhäuser Verlag Basel/Switzerland
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Vasilevski, N. (2010). Parabolic Quasi-radial Quasi-homogeneous Symbols and Commutative Algebras of Toeplitz Operators. In: Topics in Operator Theory. Operator Theory: Advances and Applications, vol 202. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0158-0_33
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DOI: https://doi.org/10.1007/978-3-0346-0158-0_33
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Publisher Name: Birkhäuser Basel
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Online ISBN: 978-3-0346-0158-0
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