On $2\times 2$ matrices over $C^\ast$-algebras

Abstract: We characterize $C^*$-algebras isomorphic to $M_2(\mathbf{C})$ and $C^*$-algebras containing $M_2(\mathbf{C})$ as a unital $C^*$-subalgebra. $*$-isomorphisms between the full $2 \times 2$ matrix algebras over $C^*$-algebras are also discussed.

Keywords: *-isomorphism of $C^*$-algebras, idempotent, projection.

Classification (MSC2000): 46L05

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