Kernel of Linear Transformation is Orthocomplement of Image of Adjoint/Corollary

Corollary to Kernel of Linear Transformation is Orthocomplement of Range of Adjoint
Let $H$ be a Hilbert space. Let $A \in B \left({H}\right)$ be a normal operator.

Then:


 * $\operatorname{ker} A = \left({\operatorname{ran} A}\right)^\perp$

where:


 * $A^*$ denotes the adjoint of $A$
 * $\operatorname{ker} A$ is the kernel of $A$
 * $\operatorname{ran} A^*$ is the range of $A^*$
 * $\perp$ signifies orthocomplementation