grandes-ecoles 2023 Q6

grandes-ecoles · France · centrale-maths1__official Not Maths
Let $a \in \mathbb{K}$. Verify that the endomorphisms $I$ and $D$ are shift-invariant, as well as the endomorphisms $E_a$, $J$ and $L$ defined in part I. Are they delta endomorphisms?
Recall: $T$ is shift-invariant if for all $a \in \mathbb{K}$, $E_a \circ T = T \circ E_a$. $T$ is a delta endomorphism if $T$ is shift-invariant and $TX \in \mathbb{K}^*$.
Let $a \in \mathbb{K}$. Verify that the endomorphisms $I$ and $D$ are shift-invariant, as well as the endomorphisms $E_a$, $J$ and $L$ defined in part I. Are they delta endomorphisms?

Recall: $T$ is shift-invariant if for all $a \in \mathbb{K}$, $E_a \circ T = T \circ E_a$. $T$ is a delta endomorphism if $T$ is shift-invariant and $TX \in \mathbb{K}^*$.