A Double Commutant Relation in the Calkin Algebra on the Bergman Space
نویسنده
چکیده
Let T be the Toeplitz algebra on the Bergman space La(B, dv) of the unit ball in C. We show that the image of T in the Calkin algebra satisfies the double commutant relation: π(T ) = {π(T )}′′. This is a surprising result, for it is the opposite of what happens in the Hardy-space case [16,17].
منابع مشابه
On the Essential Commutant of T (qc)
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 r...
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