A A C*-algebra in which invertible elements are dense.

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Consider l¥(W), the C*-algebra of all bounded mappings from a set W into C, f Î l¥(W), e > 0. If
g(t) = ì
í
î
f(t)
|f(t)| ³ e
e
|f(t)| < e
we have g Î l¥(W), ||g-f|| £ 2e. Since inf|g(t)| ³ e > 0, g is invertible.

Comment. C([a,b]) provides a separable example.


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On 22 Feb 2001, 00:18.