Bilinear forms and the $\Ext^2$-problem in Banach spaces

Jesús M. F. Castillo, Ricardo García

Let $X$ be a Banach space and let $\kappa (X)$ denote the kernel of a quotient map ${\ell }_1(\Gamma )\to X$. We show that $\Ext^2(X,X^*)=0$ if and only if bilinear forms on $\kappa (X)$ extend to $\el…