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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On inductive limits of matrix algebras of holomorphic functions
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by Justin Peters PDF
Trans. Amer. Math. Soc. 299 (1987), 303-318 Request permission

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 \[ \mathfrak {A}_n \otimes \mathcal {A}({\mathbf {D}}) \stackrel {\imath _n}{\hookrightarrow } {\mathfrak {A}_{n + 1}} \otimes \mathcal {A}({\mathbf {D}})\]. 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
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 299 (1987), 303-318
  • MSC: Primary 46L55
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0869414-8
  • MathSciNet review: 869414