A normed algebra A normed algebra A whose radical is isomorphic to C.

******************************

Suppose that A = {(
a
b
0
c
) ; a,b,c Î C }. Then A is a subalgebra of M2(C) @ B(C2) and the only its characters are f((
a
b
0
c
)) = a and g((
a
b
0
c
))) = c, since
ì
í
î
æ
ç
è
1
0
0
0
ö
÷
ø
       , æ
ç
è
0
1
0
0
ö
÷
ø
       , æ
ç
è
0
0
0
1
ö
÷
ø
ü
ý
þ
is a basis for A. Therefore Rad(A) = {(
0
b
0
0
) ; b Î C } is isometrically isomorphic to C.


File translated from TEX by TTH, version 2.70.
On 22 Feb 2001, 00:14.