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- W2907175002 abstract "It is known that Toeplitz operators, whose symbols are invariant under the action a maximal Abelian subgroups of biholomorphisms of the unit ball ( mathbb{B}^{n}), generate the C∗-algebra being commutative in each standardly weighted Bergman space. In case of the unit disk (n = 1) this condition on generating symbols is also necessary in order that the corresponding C∗-algebra be commutative. In this paper, for n > 1, we describe a wide class of symbols that are not invariant under the action of any maximal Abelian subgroup of biholomorphisms of the unit ball, and which, nevertheless, generate via corresponding Toeplitz operators C∗-algebras being commutative in each standardly weighted Bergman space. These classes of symbols are certain proper subsets of functions that are invariant under the action of the group ( mathbb{T}^{m}), with m ≤ n, being a subgroup of the maximal Abelian subgroup ( mathbb{T}^{n}) of biholomorphisms of ( mathbb{B}^{n})." @default.
- W2907175002 created "2019-01-11" @default.
- W2907175002 creator A5007791207 @default.
- W2907175002 date "2018-01-01" @default.
- W2907175002 modified "2023-10-14" @default.
- W2907175002 title "On commutative C∗-algebras generated by Toeplitz operators with $$ mathbb{T}^{m}$$ -invariant symbols" @default.
- W2907175002 doi "https://doi.org/10.1007/978-3-030-04269-1_18" @default.
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