Hilbert Spaces, Dirichlet’s Principle and Linear Compact Operators

Abstract

In a normed space, we can measure the length of a vector but not the angle formed by two vectors. This is instead possible in a Hilbert space, i.e., a Banach space whose norm is induced by an inner (or Hermitian) product. The inner (Hermitian) product allows us to measure the length of a vector, the distance between two vectors and the angle formed by them.