Riesz's lemma

For another result sometimes called Riesz's lemma, see Riesz representation theorem. For more theorems that are called Riesz's theorem, see Riesz theorem.

In mathematics, Riesz's lemma (after Frigyes Riesz) is a lemma in functional analysis. It specifies (often easy to check) conditions that guarantee that a subspace in a normed vector space is dense. The lemma may also be called the Riesz lemma or Riesz inequality. It can be seen as a substitute for orthogonality when the normed space is not an inner product space.