Bishop's Theorem and Differentiability of a subspace of $C_b(K)$

Yun Sung Choi, Han Ju Lee, Hyun Gwi Song

Let $K$ be a Hausdorff space and $C_b(K)$ be the Banach algebra of all complex bounded continuous functions on $K$. We study the Gâteaux and Fréchet differentiability of subspaces…