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Miklós Schweitzer
2015 Miklos Schweitzer
10
10
Part of
2015 Miklos Schweitzer
Problems
(1)
Operators on Hilbert Space
Source: Miklos Schweitzer 2015,P10
4/8/2016
Let
f
:
R
→
R
f:\mathbb{R}\to \mathbb{R}
f
:
R
→
R
be a continuously differentiable,strictly convex function.Let
H
H
H
be a Hilbert space and
A
,
B
A,B
A
,
B
be bounded,self adjoint linear operators on
H
H
H
.Prove that,if
f
(
A
)
−
f
(
B
)
=
f
′
(
B
)
(
A
−
B
)
f(A)-f(B)=f'(B)(A-B)
f
(
A
)
−
f
(
B
)
=
f
′
(
B
)
(
A
−
B
)
then
A
=
B
A=B
A
=
B
.
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