A remark on the deformation of GNS representations of *-algebras

Motivated by deformation quantization we investigate an algebraic GNS construction of *-representations of deformed *-algebras over ordered rings and compute their classical limit. The question whether a GNS representation can be deformed leads to deformation of positive linear functionals. Various physical examples from deformation quantization like the Bargmann—Fock and the Schrödinger representation as well as KMS functionals are discussed.