
doi: 10.1007/bf02248748
Summary: We show that a topologically irreducible \(*\) representation of a real \(C^*\)-algebra is also algebraically irreducible. Moreover, the properties of pure real states on a real \(C^*\)-algebra and their left kernels are discussed.
algebraically irreducible, General theory of \(C^*\)-algebras, States of selfadjoint operator algebras, pure real states on a real \(C^*\)-algebra and their left kernels, topologically irreducible \(*\) representation of a real \(C^*\)-algebra, transitivity theorem
algebraically irreducible, General theory of \(C^*\)-algebras, States of selfadjoint operator algebras, pure real states on a real \(C^*\)-algebra and their left kernels, topologically irreducible \(*\) representation of a real \(C^*\)-algebra, transitivity theorem
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