Homological dimensions of Banach spaces

Abstract The purpose of this paper is to lay the foundations for study problem when in Banach spaces. We provide a number examples couples $X$?> , $Y$?> such that $\operatorname{Ext}^n(X,Y)$?> (or not) $0$?> . show $\operatorname{Ext}^n(\mathcal K, \mathcal K)\neq 0$?> all $n\in \mathbb{N}$?> $\mathcal K$?> Kadec space. In particular, both projective and injective dimensions are infinite. Bibliography: 48 titles.