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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).

References [Enhancements On Off] (What's this?)

  • [1] T. W. Palmer, Spectral algebras, Rocky Mountain. J. Math. 22 (1992), 293-328. MR 93d:46079 MR 1159960 (93d:46079)
  • [2] S. C. Power, Simplicity of $ {C^{\ast}}$-algebras of minimal dynamical systems, J. London Math. Soc. (2) 18 (1978), 534-538. MR 81e:46057 MR 518239 (81e:46057)
  • [3] L. B. Schweitzer, A short proof that $ {M_n}(A)$ is local if $ A$ is local and Fréchet, Internat. J. Math. 3 (1992), 581-589. MR 93i:46082 MR 1168361 (93i:46082)

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Keywords: Spectral subalgebra, spectral invariance, irrational rotation algebra, simple Banach algebra
Article copyright: © Copyright 1994 American Mathematical Society

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