Gorenstein algebras and recollements

Let A, , and be artin algebras. We prove that if there is a recollement of the bounded Gorenstein derived category relative to the bounded Gorenstein derived categories and , then A is Gorenstein if and only if so are and . In addition, we prove that a virtually Gorenstein algebra A is Gorenstein if and only if the bounded homotopy category of (finitely generated) projective left A-modules and that of (finitely generated) injective left A-modules coincide.