Result: ROOTS OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE
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Further Information
A major goal in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex plane ℂ is to competely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. In [2007], the first author characterized the commutant of a Toeplitz operator T that has a quasihomogeneous symbol φ(r)eipθ with p > 0, in case it has a Toeplitz p-th root S with symbol ψ(r)eiθ: The commutant of T is the closure of the linear space generated by powers S that are Toeplitz. But the existence of a p-th root was known until now only when φ(r) = rm with m ≥ 0. Here we will show the existence of p-th roots for a much larger class of symbols, for example, those symbols for which where 0 < ai, bi for all 1 < i < k.