Toeplitz operators on Cartan domains essentially commute with a bilateral shift
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- by Miroslav Engliš PDF
- Proc. Amer. Math. Soc. 117 (1993), 365-368 Request permission
Abstract:
For bounded symmetric domains $\Omega \subset {{\mathbf {C}}^N}$, a bilaterial shift operator $U$ is shown to exist on the Bergman space ${A^2}(\Omega )$ such that $U{T_f} - {T_f}U$ is a compact operator for all Toeplitz operators ${T_f}$. This may be viewed as an extension of the well-known fact that ${S^{\ast }}TS - T = 0$ whenever $T$ is a Toeplitz operator on ${H^2},\;S$ being the unilateral shift. It also follows that the ${C^{\ast }}$-algebra generated by Toeplitz operators on ${A^2}(\Omega )$ does not contain all bounded operators.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 365-368
- MSC: Primary 47B35; Secondary 32M15
- DOI: https://doi.org/10.1090/S0002-9939-1993-1123651-4
- MathSciNet review: 1123651