Non-reflexive space that is isomorphic to its second dual space

Question

I was wondering if it is possible to construct a space that is non-reflexive (so it is not isomorphic to its second dual space under the cannonical embedding), but some isomorphism exists between them.

Furthermore is there a space that is not isomorphic to its second dual space, but it is isomorphic to its $n$-th dual space for some $n\in \mathbb{N} $?

Thanks in advance!

Answer 1

For your first question, you are looking for James' space (https://en.wikipedia.org/wiki/James%27_space).