A derived functor approach to bounded cohomology
The author applies some results about derived categories to the category of Banach modules over a discrete group \(G\), \(G\)-\({\mathcal B}an\). Since this category has enough injective objects, its derived category \({\mathcal D}({\mathcal B}an)\) exists and its heart is equivalent to the category of quotient Banach spaces \(q{\mathcal B}an\). Therefore, a universal \(\delta\)-functor \(\mathcal{H}^{n}:G\)-\({\mathcal B}an\to q{\mathcal B}an\) exists and this is used in Theorem 4.1 to reconstruct the bounded cohomology functors in the sense of Gromov-Brooks-Ivanov-Noskov.
scientific article; zbMATH DE number 5293449
scientific article