1. X : Banach space
Z : closed subspace of X
Prove or disprove that X* ⊆ Z*
where Z* and X* are dual space of Z and X, respectively.
2. X : normed space and f : X → R : linear functional.
Assume that ∃a∈X and r∈(0,1] such that f(B(a,r))=R(Real numbers)
where B(a,r) is open...