Abstract
We give an example of a dense, simple, unital Banach subalgebra A A of the irrational rotation C ∗ {C^{\ast }} -algebra B B , such that A A is not a spectral subalgebra of B B . This answers a question posed by T. W. Palmer (Spectral algebras, Rocky Mountain J. Math. 22 (1992), 293-328).
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