Homological dimensions of Banach spaces. (April 2021)

• Record Type: Journal Article
• Authors: Sánchez, F. Cabello; Castillo, J. M. F.; García, R.
• Is Part Of: Sbornik. Volume 212:Number 4(2021)
• Page Start: 531
• Page End: 550
• Publication Date: 2021-04
• Subjects: 46M15 -- 46M18 -- 46M10; exact sequence -- homology -- $\operatorname{Ext}^n$ functor -- Banach space -- quasi- Banach space -- homological dimension; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM9425
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: The purpose of this paper is to lay the foundations for the study of the problem of when in Banach spaces. We provide a number of examples of couples, such that is (or is not) . We show that for all when is the Kadec space. In particular, both the projective and injective dimensions of are infinite. Bibliography: 48 titles.