Pullback diagram of H∗ -algebras

Abstract

In this paper we obtain some properties for the pullback diagram of H∗ -algebras. More precisely, we prove that the commutative diagram of H∗ -algebras and morphisms A1 φ1 −−−−−→ B1   yψ1   yψ2 A2 φ2 −−−−−→ B2 is pullback and ψ1 is an injection if and only if ψ1 is a surjection, ψ2 is an injection, and ker φ1 ∩ ker ψ1 = {0}.