## Proving that a Banach space is of finite dimension

Let X be a Banach space with dimX≤∞. such that X∗ (the dual of X ) is finite dimensional. Then, show that X is of finite dimensional too and dimX=dimX∗. Note If wherenever we know that X is of finite dimensision, it is easy using linear algebra tools to show that dimX=dimX∗. Therefore the assumption … Read more