# Norm of Self-Adjoint Operator/Corollary

Jump to navigation
Jump to search

## 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

- 1990: John B. Conway:
*A Course in Functional Analysis*... (previous) ... (next) $II.2.13, 14$