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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Toeplitz operators on bounded symmetric domains


Author: Harald Upmeier
Journal: Trans. Amer. Math. Soc. 280 (1983), 221-237
MSC: Primary 47B35; Secondary 32M15, 46L99
MathSciNet review: 712257
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Abstract: In this paper Jordan algebraic methods are applied to study Toeplitz operators on the Hardy space $ {H^2}(S)$ associated with the Shilov boundary $ S$ of a bounded symmetric domain $ D$ in $ {{\mathbf{C}}^n}$ of arbitrary rank. The Jordan triple system $ Z \approx {{\mathbf{C}}^n}$ associated with $ D$ is used to determine the relationship between Toeplitz operators and differential operators. Further, it is shown that each Jordan triple idempotent $ e \in Z$ induces an irreducible representation ("$ e$-symbol") of the $ {C^{\ast} }$-algebra $ \mathcal{T}$ generated by all Toeplitz operators $ {T_f}$ with continuous symbol function $ f$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0712257-2
PII: S 0002-9947(1983)0712257-2
Article copyright: © Copyright 1983 American Mathematical Society