2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221743A classical problem in operator theory has been to determine the spectrum of Toeplitz-like operators on Hilbert spaces of vector-valued holomorphic functions on the open unit ball in C^m. In this note we obtain necessary conditions for k-tuples of such operators to be Fredholm in the sense of Taylor and show they are sufficient in the case of the unit disk.11 pages, no figureOperator AlgebrasFunctional Analysis47A13, 46E22, 46M20, 47B32text