Tauberian pairs of closed subspaces of a Banach space
Abstract
We introduce the notions of tauberian, cotauberian and weakly compact pair of closed subspaces of a Banach space. The theory produced by these notions is richer than that of the corresponding operators since an operator can be regarded as a suitable pair of closed subspaces. We investigate into these classes of pairs of subspaces and describe several applications in order to define some notions of indecomposability for Banach spaces and in order to extend definitions from the case of bounded operators to the case of closed operators.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.