Due date: November 10
Let Y be a vector subspace of the normed space X. Then its closure is also a vector subspace of X.
Let with the inner product
Apply the Gram-Schmidt process to the sequence to obtain the orthonormal polynomials , such that each is of degree n.
These are the first Legendre polynomials.
Let Y be a close subspace of the Hilbert space X and the orthogonal projection onto Y,
T is continuous.
Let Y be a closed subspace of the Hilbert space X, and let
- is a closed subspace of X.
Let X be an inner product space and its completion.
- is a Hilbert space.
- If X is separable, so is .