Integral Equations and Operator Theory

, Volume 66, Issue 1, pp 141–152

Quasi-Radial Quasi-Homogeneous Symbols and Commutative Banach Algebras of Toeplitz Operators

Article

DOI: 10.1007/s00020-009-1732-8

Cite this article as:
Vasilevski, N. Integr. Equ. Oper. Theory (2010) 66: 141. doi:10.1007/s00020-009-1732-8

Abstract

We present here a quite unexpected result: Apart from already known commutative C*-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C*-algebra, and for n = 1 all of them collapse to the algebra generated by Toeplitz operators with radial symbols.

Mathematics Subject Classification (2010)

Primary 47B35 Secondary 47L80 32A36 

Keywords

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

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Departamento de Matemáticas, CINVESTAVMéxico, D.F.México

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