Parabolic quasi-radial quasi-homogeneous symbols and commutative algebras of Toeplitz operators∗
نویسنده
چکیده
We describe new Banach (not C∗ !) algebras generated by Toeplitz operators which are commutative on each weighted Bergman space over the unit ball B, 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 inself.
منابع مشابه
Quasi-radial quasi-homogeneous symbols and commutative Banach algebras of Toeplitz operators
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 ...
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