Finitely generated algebras with involution and their identities

We consider associative algebras with involution over a field of characteristic zero. In this case, we prove that for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution which satisfies the same identities with involution. This is an analogue and an extension of the theorem of A.R. Kemer for ordinary identities (Kemer, 1991 [8], ). The similar results were proved earlier by the author for identities graded by a finite abelian group (Sviridova, 2011 [15], ), and by E. Aljadeff, and A. Kanel-Belov (2010) [1] for identities graded by any finite group.