Can someone help me to construct a linear functional in $\mathcal{C}([0,1])$ that does not attain its norm?
Actually, I want to prove that $\mathcal{C}([0,1])$ is not reflexive Banach space. Is it sufficient to construct that kind of functional?
Can someone help me to construct a linear functional in $\mathcal{C}([0,1])$ that does not attain its norm?
Actually, I want to prove that $\mathcal{C}([0,1])$ is not reflexive Banach space. Is it sufficient to construct that kind of functional?