I'm having trouble proving that $B $ is essentielly maximal accretive implies that there existes $ a>0 $ such that $(A^∗+a Id)$ is injective.
where B is the closure of the operator A and A* is the adjoint of A
Here is what i did:
we proceede by contraposition. let us suppose that for any $a>0$ we have $(A^∗+a Id)$ is not injective hence there exists $u∈D(A^∗)$ such that $A^∗u=−au$ hence $<A^∗u,u>=−a||u||^2 $ or $<A^∗u,u>=<B^∗u,u>$ but I could not conclude.