A Non-Spectral Dense Banach Subalgebra of the Irrational Rotation Algebra
Abstract
We give an example of a dense, simple, unital Banach subalgebra
A
of the irrational rotation C*-algebra
B
, such that
A
is not a spectral subalgebra of
B
. This answers a question posed in T.W. Palmer's paper [1].