An element An element x of a Banach algebra such r(x) < ||x ||.

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Consider x = [
0
1
0
0
] in the C*-algebra M2(C) @ B(C2). Then sp(x) = {0}. So r(x) = 0. But ||x || = 1 (since its associated operator T(z1,z2) = (z2,0) has norm 1).


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On 22 Feb 2001, 00:14.