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Found problems: 1

2015 Miklos Schweitzer, 10
Tags: functional analysis , spectral analysis
Let $f:\mathbb{R}\to \mathbb{R}$ be a continuously differentiable,strictly convex function.Let $H$ be a Hilbert space and $A,B$ be bounded,self adjoint linear operators on $H$.Prove that,if $f(A)-f(B)=f'(B)(A-B)$ then $A=B$.