Then (X, ⟨., .⟩) is an inner product space.

In this chapter, we will discuss the fundamental concepts of functional analysis, including vector spaces, linear operators, and inner product spaces.

for any f in X and any x in [0, 1]. Then T is a linear operator.

Tf(x) = ∫[0, x] f(t)dt

||f||∞ = maxf(x).

⟨f, g⟩ = ∫[0, 1] f(x)g(x)̅ dx.

Here are some exercise solutions: