Pullback diagram of H^*-algebras

Authors: MAHNAZ KHANEHGIR, MARYAM AMYARI, MARZIEH MORADIAN KHIBARY

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 A_1 @>\varphi_1>> B_1 @VV\psi_1V @VV\psi_2V A_2 @>\varphi_2>> B_2 is pullback and \psi_1 is an injection if and only if \psi_1 is a surjection, \psi_2 is an injection, and \ker \varphi_1 \cap \ker \psi_1 = \{0\}.

Keywords: H^*-algebra, morphisms, pullback diagram, trace-class

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