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- W2000771250 abstract "Let T ∈ B ( H ) n be an essentially normal spherical isometry with empty point spectrum on a separable complex Hilbert space H , and let A T ⊂ B ( H ) be the unital dual operator algebra generated by T . In this note we show that every operator S ∈ B ( H ) in the essential commutant of A T has the form S = X + K with a T -Toeplitz operator X and a compact operator K . Our proof actually covers a larger class of subnormal operator tuples, called A -isometries, which includes for example the tuple T = ( M z 1 , … , M z n ) ∈ B ( H 2 ( σ ) ) n consisting of the multiplication operators with the coordinate functions on the Hardy space H 2 ( σ ) associated with the normalized surface measure σ on the boundary ∂ D of a strictly pseudoconvex domain D ⊂ C n . As an application we determine the essential commutant of the set of all analytic Toeplitz operators on H 2 ( σ ) and thus extend results proved by Davidson (1977) [6] for the unit disc and Ding and Sun (1997) [11] for the unit ball." @default.
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- W2000771250 date "2011-09-01" @default.
- W2000771250 modified "2023-09-27" @default.
- W2000771250 title "On the essential commutant of analytic Toeplitz operators associated with spherical isometries" @default.
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- W2000771250 doi "https://doi.org/10.1016/j.jfa.2011.05.005" @default.
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