Huaxin Lin
Abstract
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Let A A be a non-unital and Ο \sigma -unital simple C β C^* -algebra. We show that if M ( A ) / A M(A)/A is simple, then M ( A ) / A M(A)/A is purely infinite. We also show that M ( A ) / A M(A)/A is simple if and only if A A has a continuous scale provided that A A is not isomorphic to K , {\mathcal K}, the compact operators.
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Let A A be a non-unital and Ο \sigma -unital simple C β C^* -algebra. We show that if M ( A ) / A M(A)/A is simple, then M ( A ) / A M(A)/A is purely infinite. We also show that M ( A ) / A M(A)/A is simple if and only if A A has a continuous scale provided that A A is not isomorphic to K , {\mathcal K}, the compact operators.
Key concepts: Unital, Simple (philosophy), Mathematics, Pure mathematics, Scale (ratio), Algebra over a field, Discrete mathematics, Physics