کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590989 | 1334999 | 2011 | 23 صفحه PDF | دانلود رایگان |
Let T∈Bn(H) be an essentially normal spherical isometry with empty point spectrum on a separable complex Hilbert space H, and let AT⊂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 AT 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=(Mz1,…,Mzn)∈B(H2n(σ)) consisting of the multiplication operators with the coordinate functions on the Hardy space H2(σ) associated with the normalized surface measure σ on the boundary ∂D of a strictly pseudoconvex domain D⊂Cn. As an application we determine the essential commutant of the set of all analytic Toeplitz operators on H2(σ) and thus extend results proved by Davidson (1977) [6], for the unit disc and Ding and Sun (1997) [11] for the unit ball.
Journal: Journal of Functional Analysis - Volume 261, Issue 5, 1 September 2011, Pages 1361-1383