Norm of Self-Adjoint Operator/Corollary

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Corollary to Norm of Self-Adjoint Operator

Let $H$ be a Hilbert space.

Let $A \in \map B H$ be a self-adjoint operator.


Suppose also that:

$\forall h \in H: \sequence {A h, h}_H = 0$



Then $A$ is the zero operator $\mathbf 0$.


Proof


Sources