Show that the set of shift-invariant endomorphisms of $\mathbb{K}[X]$ is a subalgebra of $\mathcal{L}(\mathbb{K}[X])$. Is the set of delta endomorphisms of $\mathbb{K}[X]$ closed under addition? under composition?
Show that the set of shift-invariant endomorphisms of $\mathbb{K}[X]$ is a subalgebra of $\mathcal{L}(\mathbb{K}[X])$. Is the set of delta endomorphisms of $\mathbb{K}[X]$ closed under addition? under composition?