Functional Analysis Answers

show that f°f=2f

f=x+1

Let H be a Hilbert space.

(i) Let S ⊆ H be any non-empty subset of S. Show that S ^⊥ is a subspace of H.

(ii) Let L ⊆ H be a linear manifold. Show that L^ ⊥⊥ = L

(i) Let V be a Banach space and let L ⊆ V be a linear manifold. Show that L, the closure of L, is a subspace of V .

(ii) Let H be a Hilbert space. Let B be an orthonormal set in H. Show that span B is dense in H if and only if B is an orthonormal basis.

Prove that every (non-zero) Hilbert space H has an orthonormal basis.

B(T) is separable iff T is finite.prove it

Show that L^infinity is not separable space

a) What is proposition?

b.) P and q are propositions given by p: f is an odd function and q: ∫𝑓(𝑥)𝑑𝑥=0𝑘−𝑘

verify whether or not 𝑝↔𝑞