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user1688
user1688

You could have googledIf you google "representations of the Calkin algebra" which would have led, you tofind the 1967 paper of Sakai which answers your question in the negative: It says that the Calkin algebra has a type III factor representation. By the Lemma of Schur, however, every irrducible representation is a type I representation and a direct sum of more than one irreducible is not a factor.

You could have googled "representations of the Calkin algebra" which would have led you to the 1967 paper of Sakai which answers your question in the negative: It says that the Calkin algebra has a type III factor representation. By the Lemma of Schur, however, every irrducible representation is a type I representation and a direct sum of more than one irreducible is not a factor.

If you google "representations of the Calkin algebra", you find the 1967 paper of Sakai which answers your question in the negative: It says that the Calkin algebra has a type III factor representation. By the Lemma of Schur, however, every irrducible representation is a type I representation and a direct sum of more than one irreducible is not a factor.

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user1688
user1688

You could have googled "representations of the Calkin algebra" which would have led you to the 1967 paper of Sakai which answers your question in the negative: It says that the Calkin algebra has a type III factor representation. By the Lemma of Schur, however, every irrducible representation is a type I representation and a direct sum of more than one irreducible is not a factor.