Polynomial identities play a crucial role in algebraic structures, and the study of Hilbert series has been important in understanding the properties of algebras. While the Hilbert-Serre theorem states that the Hilbert series of a finitely generated commutative algebra is rational, this is not true for non-commutative algebras. However, there are classes of non-commutative algebras, such as relatively free algebras, for which the Hilbert series is rational. The authors aim to study the Hilbert series of T-spaces, which are vector subspaces of free associative algebras generated by polynomials closed under substitutions. The main result of the paper provides conditions under which the Hilbert series of a T-space is rational or differs from the Hilbert series of the commutator by a rational function. The research is motivated by the desire to understand the behavior of Hilbert series in T-spaces and its implications for algebraic structures.