Manuilov algebra, \(C^\ast\)-Hilbert modules, and Kuiper type theorems (Q1714009)

The author generalizes the $C^*$-algebra generated by matrices of bounded operators in a separable Hilbert space $H$ with a uniformly bounded number of nonzero elements in each row and each column with respect to a fixed basis, introduced recently by the reviewer [``On the $C^*$-algebra of matrix-finite bounded operators'', Preprint, \url{arXiv:1807.11020}], to the case of Hilbert $C^*$-modules. The main result of the paper is contractibility of the groups of invertible elements in these generalized $C^*$- or Banach algebras (Kuiper-type theorems).