An element
An element x of a Banach algebra such r(x) <
||
x
||
.
******************************
Consider x = [
0
1
0
0
] in the C
*
-algebra M
2
(
C
)
@
B(
C
2
). Then sp(x) = {0}. So r(x) = 0. But
||
x
||
= 1 (since its associated operator T(z
1
,z
2
) = (z
2
,0) has norm 1).
File translated from T
E
X by
T
T
H
, version 2.70.
On 22 Feb 2001, 00:14.