## 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.## References

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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