Two element
Two element a, b of a Banach algebra such that neither r(ab)
£
r(a)r(b) nor r(a+b)
£
r(a)r(b).
******************************
Consider a = [
0
1
0
0
] and b = [
0
0
1
0
] in M
2
(
C
)
@
B(
C
2
). Then sp(a) = {0}, sp(b) = {0},sp(a+b) = {
-
1,1}, sp(ab) = {0,1} and we have required inequalities.
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T
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, version 2.70.
On 22 Feb 2001, 00:14.