A nonspectral dense Banach subalgebra of the irrational rotation algebra
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- by Larry B. Schweitzer PDF
- Proc. Amer. Math. Soc. 120 (1994), 811-813 Request permission
Abstract:
We give an example of a dense, simple, unital Banach subalgebra $A$ of the irrational rotation ${C^{\ast }}$-algebra $B$, such that $A$ is not a spectral subalgebra of $B$. This answers a question posed by T. W. Palmer (Spectral algebras, Rocky Mountain J. Math. 22 (1992), 293-328).References
- Theodore W. Palmer, Spectral algebras, Rocky Mountain J. Math. 22 (1992), no. 1, 293–328. MR 1159960, DOI 10.1216/rmjm/1181072812
- S. C. Power, Simplicity of $C^{\ast }$-algebras of minimal dynamical systems, J. London Math. Soc. (2) 18 (1978), no. 3, 534–538. MR 518239, DOI 10.1112/jlms/s2-18.3.534
- Larry B. Schweitzer, A short proof that $M_n(A)$ is local if $A$ is local and Fréchet, Internat. J. Math. 3 (1992), no. 4, 581–589. MR 1168361, DOI 10.1142/S0129167X92000266
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 811-813
- MSC: Primary 46L05; Secondary 46H20
- DOI: https://doi.org/10.1090/S0002-9939-1994-1179591-9
- MathSciNet review: 1179591