Geodesic
Homological dimensions of Banach spaces
Sbornik. Mathematics, Tome 212 (2021) no. 4, pp. 531-550

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The purpose of this paper is to lay the foundations for the study of the problem of when $\operatorname{Ext}^n(X, Y)=0$ in Banach spaces. We provide a number of examples of couples $X$, $Y$ such that $\operatorname{Ext}^n(X,Y)$ is (or is not) $0$. We show that $\operatorname{Ext}^n(\mathcal K, \mathcal K)\neq 0$ for all $n\in \mathbb{N}$ when $\mathcal K$ is the Kadec space. In particular, both the projective and injective dimensions of $\mathcal K$ are infinite. Bibliography: 48 titles.
Keywords: exact sequence, homology, $\operatorname{Ext}^n$ functor, Banach space
Mots-clés : quasi-Banach space, homological dimension. 
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     author = {F. Cabello S\'anchez and J. M. F. Castillo and R. Garc{\'\i}a},
     title = {Homological dimensions of {Banach} spaces},
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     url = {http://geodesic.mathdoc.fr/item/SM_2021_212_4_a4/}
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F. Cabello Sánchez; J. M. F. Castillo; R. García. Homological dimensions of Banach spaces. Sbornik. Mathematics, Tome 212 (2021) no. 4, pp. 531-550. http://geodesic.mathdoc.fr/item/SM_2021_212_4_a4/