Is the Laplace operator dissipative?

Question

Consider the Banach space $C_\infty(\mathbb{R}^n) = \{f \in C(\mathbb{R}^n) \mid \lim_{|x| \to \infty} f(x) = 0\}$ equipped with the supremum norm $||\cdot||_\infty$. My question is wether the Laplace operator $\Delta:C_c^2(\mathbb{R}^n) \to C_\infty(\mathbb{R}^n)$ is dissipative, that is, that for all $\lambda>0$ and any $f \in C_c^2(\mathbb{R}^n)$ we have $$ ||\lambda f - \Delta f||_\infty \geq \lambda ||f||_\infty.$$ Any ideas?