When does $C(K,X)$ contain a complemented copy of $c_0(\Gamma )$ iff $X$ does?

Elói Medina Galego, Vinícius Morelli Cortes

Let $K$ be a compact Hausdorff space with weight w$(K)$, $\tau$ an infinite cardinal with cofinality cf$(\tau )$ and $X$ a Banach space. In contrast with a classical theorem of Cembranos…