On the Essential Commutant of T (qc)
نویسنده
چکیده
Let T (QC) (resp. T ) be the C∗-algebra generated by the Toeplitz operators {Tφ : φ ∈ QC} (resp. {Tφ : φ ∈ L∞}) on the Hardy space H2 of the unit circle. A well-known theorem of Davidson asserts that T (QC) is the essential commutant of T . We show that the essential commutant of T (QC) is strictly larger than T . Thus the image of T in the Calkin algebra does not satisfy the double commutant relation. We also give a criterion for membership in the essential commutant of T (QC).
منابع مشابه
Singular Integral Operators and Essential Commutativity on the Sphere
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تاریخ انتشار 2007