A note on Gorenstein projective complexes

As we know, a complex Q is projective if and only if Q is exact and Z(n)(Q) is projective in R-Mod for each n is an element of Z. In this article, we show that a complex G is Gorenstein projective with Hom(R) (P, G) and Hom(R) (G,P) exact for any Cartan-Eilenberg projective complex P if and only if G is exact and Z(n)(G) is Gorenstein projective in R-Mod for each n is an element of Z. Using the above result, a new equivalent characterization of some A complexes is obtained.