On the essential commutant of analytic Toeplitz operators associated with spherical isometries
In: Journal of Functional Analysis, Jg. 261 (2011-09-01), Heft 5, S. 1361-1383
academicJournal
Zugriff:
Abstract: Let be an essentially normal spherical isometry with empty point spectrum on a separable complex Hilbert space H, and let be the unital dual operator algebra generated by T. In this note we show that every operator in the essential commutant of has the form 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 consisting of the multiplication operators with the coordinate functions on the Hardy space associated with the normalized surface measure σ on the boundary ∂D of a strictly pseudoconvex domain . As an application we determine the essential commutant of the set of all analytic Toeplitz operators on and thus extend results proved by Davidson (1977) for the unit disc and Ding and Sun (1997) for the unit ball. [Copyright &y& Elsevier]
Titel: |
On the essential commutant of analytic Toeplitz operators associated with spherical isometries
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Autor/in / Beteiligte Person: | Didas, Michael ; Eschmeier, Jörg ; Everard, Kevin |
Zeitschrift: | Journal of Functional Analysis, Jg. 261 (2011-09-01), Heft 5, S. 1361-1383 |
Veröffentlichung: | 2011 |
Medientyp: | academicJournal |
ISSN: | 0022-1236 (print) |
DOI: | 10.1016/j.jfa.2011.05.005 |
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