2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163825We prove an index theorem for Toeplitz operators on the quarter-plane using the index theory for generalized Toeplitz operators introduced by G. J. Murphy. To prove this index theorem we construct an indicial triple on the tensor product of two C*-algebras provided with indicial triples with general conditions. We show that our results can be extended to some extensions of the theory of Toeplitz operators on the quarter-plane.12 pagesOperator Algebrastext