Spaces

b show that every inner product space is a normed space and every hilbert space is banach space and the converses of both the statements may not be true give examples 71607

Let H be a Hilbert space, M ⊂H a convex subset, and (xn) a sequence in M such that xn ⟶d, where d=infx ∈Mx . Show that (xn) converges in H. Give an illustrative example in 𝐑^2 or 𝐑^3. | Numerade