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

 

On inductive limits of matrix algebras of holomorphic functions


Author: Justin Peters
Journal: Trans. Amer. Math. Soc. 299 (1987), 303-318
MSC: Primary 46L55
MathSciNet review: 869414
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Abstract: Let $ \mathfrak{A}$ be a UHF algebra and $ \mathcal{A}({\mathbf{D}})$ the disk algebra. If $ \mathfrak{A} = {\left[ {{ \cup _{n \geq 1}}{\mathfrak{A}_n}} \right]^ - }$ and $ \alpha $ is a product-type automorphism of $ \mathfrak{A}$ which leaves each $ {\mathfrak{A}_n}$ invariant, then $ \alpha $ defines an embedding

$\displaystyle \mathfrak{A}_n \otimes \mathcal{A}({\mathbf{D}}) \stackrel{\imath_n}{\hookrightarrow} {\mathfrak{A}_{n + 1}} \otimes \mathcal{A}({\mathbf{D}})$

. The inductive limit of this system is a Banach algebra whose maximal ideal space is closely related to that of the disk algebra if the Connes spectrum $ \Gamma (\alpha )$ is finite.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0869414-8
PII: S 0002-9947(1987)0869414-8
Article copyright: © Copyright 1987 American Mathematical Society