2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74565We consider functors from the category of locally convex algebras to abelian groups and prove invariance under smooth homotopies for weakly J-stable algebras, where J is a harmonic operator ideal. This applies in particular to negative algebraic K-theory. We develop the technology of Kasparov modules in an algebraic setting in order to obtain the results. The article also includes a computation of the first algebraic K-theory of harmonic operator ideals.K-Theory and HomologyOperator Algebras18G, 19K, 46H, 46L80, 46M, 58B34text