vector space and its dual space
Q1. Let V be a vector space. V* be it's dual space i.e. set of all linear functions on V. W is a sub-space of V. W* be dual space of W i.e. set of all linear functions on W. Am I correct in saying that V* is a sub-space of W*? Because every f in V* will also be in W*.
I know I'm wrong but just not getting this.
Q2. Let V, V*, V** be vector space, it's dual space and it's double dual space. Can anyone help me construct a homomorphism from V* into V**, kernel of the homomorphism = A(W) annihilator of a sub-space of W, thus subspace of V*. I would want to prove that this homomorphism is onto W**. And thus derive the result that V*/A(W) is isomorphic to W** and hence W.
Thanks for reading and any help.