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Singular Integral Operators and Essential Commutativity on the Sphere

  • Jingbo Xia (a1)
Abstract

Let 𝒯 be the C*-algebra generated by the Toeplitz operators {T 𝜑 : 𝜑 Є L (S, dσ)} on the Hardy space H 2(S) of the unit sphere in C n . It is well known that 𝒯 is contained in the essential commutant of {T 𝜑 : 𝜑 Є VMO∩L (S, dσ)}. We show that the essential commutant of {T 𝜑 : 𝜑 Є VMO∩L (S, dσ)} is strictly larger than 𝒯.

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References
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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