Abstract.
Using the joint local mean oscillation, Jingbo Xia [13] showed that the essential commutant of \(\mathfrak{T}(\mathcal{L})\), where \({\mathcal{L}}\) is the subalgebra of L ∞ generated by all functions which are bounded and have at most one discontinuity, is \(\mathfrak{T}\) (QC). Even though Xia’s method cannot be used, we are able to generalize his result to Toeplitz operators in higher dimensions with a different approach. This result is stronger than the well-known result stating that the essential commutant of the full Toeplitz algebra \({\mathfrak{T}}\) is \({\mathfrak{T}}\) (QC).
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Le, T. On the Essential Commutant of Toeplitz Operators in Several Complex Variables. Integr. equ. oper. theory 59, 555–578 (2007). https://doi.org/10.1007/s00020-007-1527-8
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DOI: https://doi.org/10.1007/s00020-007-1527-8