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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A nonspectral dense Banach subalgebra of the irrational rotation algebra


Author: Larry B. Schweitzer
Journal: Proc. Amer. Math. Soc. 120 (1994), 811-813
MSC: Primary 46L05; Secondary 46H20
MathSciNet review: 1179591
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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).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1179591-9
PII: S 0002-9939(1994)1179591-9
Keywords: Spectral subalgebra, spectral invariance, irrational rotation algebra, simple Banach algebra
Article copyright: © Copyright 1994 American Mathematical Society