Let X and Y be normed vector spaces, let T be an element of the normed vector space B(X, Y ) of bounded linear operators from X to Y , and let T′ be its adjoint in B(Y′, X′). Prove the following result:

If T′Y′ is finite-dimensional then Cl(T′Y′)= ker(T )◦

That should be my last annihilator question...

Many thanks.