2025/05/12 by Brian Villegas-Villalpando, Villegas-Villalpando, Brian, Koen van den Dungen +1
Mathematics · #Advanced Operator Algebra Research #Spectral Theory in Mathematical Physics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2505.07568
We investigate complexes of Hilbert C*-modules, which are cochain complexes with (unbounded) regular operators between Hilbert C*-modules as differential maps. In particular, we provide various equivalent characterizations of the Fredholm property for such complexes of Hilbert C*-modules, and we define the Fredholm index taking values in the K-theory group of the C*-algebra. Among other properties of this index, we prove the stability under small or relatively compact perturbations, and we obtain alternative expressions for the index under the existence of a (weak or strong) Hodge decomposition.