Let $A$ a linear operator from his domaine $D(A)\subset H$ to $H$, with $H$ is a Hilbert space, such that $A$ is dissipative.

is it true that : if $\|y\|\leq \|z\|$ then $\|Ay\|\leq \|Az\|$

Let $A$ a linear operator from his domaine $D(A)\subset H$ to $H$, with $H$ is a Hilbert space, such that $A$ is dissipative.

is it true that : if $\|y\|\leq \|z\|$ then $\|Ay\|\leq \|Az\|$?

Thank you