2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160621Characterization of the *-subalgebras in the algebra of bounded operators acting on Hilbert space is presented. Sufficient conditions for the existence of a faithful representation in pre-Hilbert space of a *-algebra in terms of its Groebner basis are given. These conditions are generalization of the unshrinkability of monomial *-algebras introduced by C. Lance and P. Tapper. The applications to *-doubles, monomial *-algebras and several other classes of *-algebras are presented.revised; typos corrected, references addedOperator AlgebrasRepresentation Theory46L05,06F25text