  Characterization 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.
