# Kernel and Range of a linear operator

• March 7th 2009, 11:23 AM
HTale
Kernel and Range of a linear operator
Hey guys,

Let $A$ be a linear operator from a vector space $X$ into a vector space $Y$, and define also $\mathcal{B}(X,Y)$ as the vector space of all bounded linear operators. Now, a set of notes claims the following

"If $X$ and $Y$ are normed spaces, and $A \in \mathcal{B}(X,Y)$, then Ker $(A)$ is closed; this is not necessarily true for Ran $(A)$."

Why is this the case?