Infinity norm and operator norm question

Question

Suppose a matrix $A$ and a vector $v$ are given for appropriate size. In the Euclidean norm $\| \cdot \|_2$, we know that $$\|A v\|_2 \le \|A\|_{\text{op}} \cdot \|v\|_2$$ where $\|A\|_{\text{op}}$ is an operator norm of a matrix $A$. In a case of the infinity norm $\| \cdot \|_\infty$, does the similar result hold? That is, is the following true? $$\|A v\|_\infty \le \|A\|_{\text{op}} \cdot \|v\|_\infty$$ If not, how can we bound $\|A v\|_\infty$?