Two selfadjoint operators Two selfadjoint operators T and S on a Hilbert space such that sp(ST) is not a subset of Â.

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Consider
S = æ
ç
è
0
1
1
0
ö
÷
ø 		, T = æ
ç
è
1
0
0
-1
ö
÷
ø
belonging to B(C2). Then S and T are Hermetian, but sp(ST) = {i, -i} which is not a subset of Â.

File translated from TEX by TTH, version 2.70.
On 22 Feb 2001, 00:21.